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# Documents  14J70 | enregistrements trouvés : 31

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## Automorphisms of hyperkähler manifolds​ - Lecture 1 Sarti, Alessandra | CIRM H

Post-edited

Research talks;Algebraic and Complex Geometry

In the 80's Beauville generalized several foundational results of Nikulin on automorphism groups of K3 surfaces to hyperkähler manifolds. Since then the study of automorphism groups of hyperkähler manifolds and in particular of hyperkähler fourfolds got very much attention. I will present some classification results for automorphisms on hyperkähler fourfolds that are deformation equivalent to the Hilbert scheme of two points on a K3 surface and describe some explicit examples. I will give particular attention to double EPW sextics, that admit in a natural way a non-symplectic involution. Time permitting I will show how the rich geometry of double EPW sextics has an important connection to a classical question of U. Morin (1930). In the 80's Beauville generalized several foundational results of Nikulin on automorphism groups of K3 surfaces to hyperkähler manifolds. Since then the study of automorphism groups of hyperkähler manifolds and in particular of hyperkähler fourfolds got very much attention. I will present some classification results for automorphisms on hyperkähler fourfolds that are deformation equivalent to the Hilbert scheme of two points on a K3 surface and ...

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## Stable rationality - Lecture 1 Pirutka, Alena | CIRM H

Post-edited

Research talks;Algebraic and Complex Geometry

Let X be a smooth and projective complex algebraic variety. Several notions, describing how close X is to projective space, have been developed: X is rational if an open subset of X is isomorphic to an open of a projective space, X is stably rational if this property holds for a product of X with some projective space, and X is unirational if X is rationally dominated by a projective space. A classical Lüroth problem is to find unirational nonrational varieties. This problem remained open till 1970th, when three types of such examples were produced: cubic threefolds (Clemens and Griffiths), some quartic threefolds (Iskovskikh and Manin), and some conic bundles (Artin et Mumford). The last examples are even not stably rational. The stable rationality of the first two examples was not known.
In a recent work C. Voisin established that a double solid ramified along a very general quartic is not stably rational. Inspired by this work, we showed that many quartic solids are not stably rational (joint work with J.-L. Colliot-Thélène). More generally, B. Totaro showed that a very general hypersurface of degree d is not stably rational if d/2 is at least the smallest integer not smaller than (n+2)/3. The same method allowed us to show that the rationality is not a deformation invariant (joint with B. Hassett and Y. Tschinkel).
In this series of lectures, we will discuss the methods to obtain the results above: the universal properties of the Chow group of zero-cycles, the decomposition of the diagonal, and the specialization arguments.
Let X be a smooth and projective complex algebraic variety. Several notions, describing how close X is to projective space, have been developed: X is rational if an open subset of X is isomorphic to an open of a projective space, X is stably rational if this property holds for a product of X with some projective space, and X is unirational if X is rationally dominated by a projective space. A classical Lüroth problem is to find unirational ...

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## Algebraic cycles on varieties over finite fields Pirutka, Alena | CIRM H

Post-edited

Research talks;Algebraic and Complex Geometry

Let $X$ be a projective variety over a field $k$. Chow groups are defined as the quotient of a free group generated by irreducible subvarieties (of fixed dimension) by some equivalence relation (called rational equivalence). These groups carry many information on $X$ but are in general very difficult to study. On the other hand, one can associate to $X$ several cohomology groups which are "linear" objects and hence are rather simple to understand. One then construct maps called "cycle class maps" from Chow groups to several cohomological theories.
In this talk, we focus on the case of a variety $X$ over a finite field. In this case, Tate conjecture claims the surjectivity of the cycle class map with rational coefficients; this conjecture is still widely open. In case of integral coefficients, we speak about the integral version of the conjecture and we know several counterexamples for the surjectivity. In this talk, we present a survey of some well-known results on this subject and discuss other properties of algebraic cycles which are either proved or expected to be true. We also discuss several involved methods.
Let $X$ be a projective variety over a field $k$. Chow groups are defined as the quotient of a free group generated by irreducible subvarieties (of fixed dimension) by some equivalence relation (called rational equivalence). These groups carry many information on $X$ but are in general very difficult to study. On the other hand, one can associate to $X$ several cohomology groups which are "linear" objects and hence are rather simple to ...

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## Algebraic groups: structure ans actions.2015 Clifford lectures on algebraic groups: structure and actionsNew Orleans # March 2-5, 2015 Can, Mahir Bilen | American Mathematical Society 2017

Congrès

- vii; 294 p.
ISBN 978-1-4704-2601-9

Proceedings of symposia in pure mathematics , 0094

Localisation : Collection 1er étage

théorie des groupes # groupe algébrique différentiel # théorie des champs # géométrie birationnelle # groupe de Cremona # hypersurface # variété # variété de Toric # polyhèdre de Newton

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## Algebraic geometry and number theory:summer schoolIstanbul # 2014 Mourtada, Hussein ; Sarioglu, Celal Cem ; Soulé, Christophe ; Zeytin, Ayberk | Birkhäuser 2017

Congrès

- x; 232 p.
ISBN 978-3-319-47778-7

Progress in mathematics , 0321

Localisation : Collection 1er étage

géométrie algébrique # théorie des nombres # algèbre commutative

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## Séminaire Bourbaki. Vol. 2012/2013: exposés 1059-1073 | Société Mathématique de France 2014

Congrès

- x; 520 p.
ISBN 978-2-85629-785-8

Astérisque , 0361

Localisation : Périodique 1er étage

actions commensurantes # algèbre de Steenrod # algèbres de Lie semi-simple # bases canoniques # biparti # caractère # carte # cartes de mots # catégorification # classification # cohomologie étale # cohomologie galoisienne # cohomologie motivique # commutateurs # complexe des courbes # conjecture de Baum-Connes # conjecture de Bloch-Kato # conjecture de Hodge # conjecture d'Ore # conjecture de Thompson # constantes de Siegel-Veech # corps d'Okounkov # courbure # cycles algébriques # déterminant du laplacien diagramme de Young # différentielles holomorphes # dimension d'Iitaka # distance de Wasserstein # dynamique symbolique # échanges d'intervalles # ÉDP d'évolution # ÉDP stochastiques # endoscopie tordue # équations F-KPP # espace de modules de différentielles quadratiques # espaces métriques mesurés # exposants de Lyapunov # extrêmes # flot de la chaleur # flot géodésique de Teichmüller # flots de gradient # fonction de Hilbert # fonctorialité # formes automorphes de carré intégrable # graphe expanseur # groupe hyperbolique # groupes approximativement finis # groupes classiques # groupes élémentairement moyennables # groupes kleiniens # groupes moyennables # groupes pleins-topologiques # groupes quantiques # homéomorphismes minimaux # hyperbolicité au sens de Kobayashi # inégalités de Morse holomorphes # KK-théorie # K-théorie de Milnor # laminations terminales # mouvement brownien branchant # odomètres # partition # polynôme de Kerov propriété (T) # renormalisation # sous-décalages topologiques # surfaces plates # symétriseur de Young # théorie homotopique des schémas # trajectoires rugueuses # unicellulaire # variations de structure de Hodge actions commensurantes # algèbre de Steenrod # algèbres de Lie semi-simple # bases canoniques # biparti # caractère # carte # cartes de mots # catégorification # classification # cohomologie étale # cohomologie galoisienne # cohomologie motivique # commutateurs # complexe des courbes # conjecture de Baum-Connes # conjecture de Bloch-Kato # conjecture de Hodge # conjecture d'Ore # conjecture de Thompson # constantes de Siegel-Veech # corps ...

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## Contributions to algebraic geometry:Impanga lecture notes.Based on the Impanga conference on algebraic geometryBedlewo # july 4-10, 2010 Pragacz, Piotr | European Mathematical Society 2012

Congrès

- xii; 504 p.
ISBN 978-3-03719-114-9

Series of congress reports

Localisation : Colloque 1er étage (BEDL)

géométrie algébrique # Zariski # surface K3 # surface de Enriques # variétés de Calabi-Yau # système linéaire # constante de Seshadri # forme différentielle # théorie de Mori # anneau canonique # nombres de Hodge # forme différentielle logarithmique # variétés de Prym # espace de module # déterminant de Wron # ODE linéaire # calculus de Schubert # Grassmannien # variétés de Schubert # fonction de Schur # singularités # polynôme de Thom # P-idéal # variétés torique # variétés symplectique # quotient symplectique # cohomologie équivariente # groupe de Bloch # norme # extention de corps géométrie algébrique # Zariski # surface K3 # surface de Enriques # variétés de Calabi-Yau # système linéaire # constante de Seshadri # forme différentielle # théorie de Mori # anneau canonique # nombres de Hodge # forme différentielle logarithmique # variétés de Prym # espace de module # déterminant de Wron # ODE linéaire # calculus de Schubert # Grassmannien # variétés de Schubert # fonction de Schur # singularités # polynôme de Thom # P-idéal ...

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## Topology of algebraic varieties and singularities.Conference in honor of Anatoly Libgober's 60th birthdayHuesca # june 22-26, 2009 Cogolludo-Agustin, José Ignacio ; Hironaka, Eriko | American Mathematical Society;Real Sociedad Matematica Espanola 2011

Congrès

- xxiv; 467 p.
ISBN 978-0-8218-4890-6

Contemporary mathematics , 0538

Localisation : Collection 1er étage

géométrie algébrique # singularités # hypersurfaces algébriques # arrangements de sous-espaces linéaires # anatoly Libgober

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## Algorithms in algebraic geometrybased on the workshopMinneapolis # september 18-22, 2006 Dickenstein, Alicia ; Schreyer, Frank-Olaf ; Sommese, Andrew J. | Springer 2008

Congrès

- xi; 157 p.
ISBN 978-0-387-75154-2

the IMA volumes in mathematics and its applications , 0146

Localisation : Colloque 1er étage (MINN)

géométrie algébrique # algorithme # analyse numérique # calcul formel

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## Séminaire de géométrie analytique 1968-1969 Bloom ; Mazet ; Moulis ; Ramis ; Ruget, Claudine | Faculté des Sciences d'Orsay 1969

Congrès

- pag. mult.

Publications Mathématiques d'Orsay

Localisation : Salle de manutention

anneau de cohomologie # codimension topologique # complexe dualisant # ensemble d'opérateurs à indice # espace analytique de dimension infinie # espace de Hilbert complexe # germe analytique banachique # géométrie analytique banachique # intersection # nullstellensatz # opérateur à indice # singularité d'hypersurface # situation analytique épidermique # théorème d'image directe # théorème de dualité # variété hilbertienne de dimension infinie

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## Journées singulières et jacobiennesséminaire d'algèbre et géométrieMai 26-28 | Institut Fourier;Université de Grenoble I 1993

Congrès

Localisation : Disparu

algèbre et géométrie # amas torique # courbe cuspidale plane # diviseur exceptionnel # famille d'hypersurface contractible en C puissance 4 # feuilletage # filtration par idéal complet # idéal complet # inégalité d'intersection # polynôme à fibre lisse irréductible # proximité # surface algébrique # système linéaire # théorie de Zariski-Lipman

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## A Grassmannian technique and the Kobayashi Conjecture Riedl, Eric | CIRM H

Multi angle

Research talks

An entire curve on a complex variety is a holomorphic map from the complex numbers to the variety. We discuss two well-known conjectures on entire curves on very general high-degree hypersurfaces $X$ in $\mathbb{P}^n$: the Green-Griffiths-Lang Conjecture, which says that the entire curves lie in a proper subvariety of $X$, and the Kobayashi Conjecture, which says that X contains no entire curves.
We prove that (a slightly strengthened version of) the Green-Griffiths-Lang Conjecture in dimension $2n$ implies the Kobayashi Conjecture in dimension $n$. The technique has already led to improved bounds for the Kobayashi Conjecture. This is joint work with David Yang.
An entire curve on a complex variety is a holomorphic map from the complex numbers to the variety. We discuss two well-known conjectures on entire curves on very general high-degree hypersurfaces $X$ in $\mathbb{P}^n$: the Green-Griffiths-Lang Conjecture, which says that the entire curves lie in a proper subvariety of $X$, and the Kobayashi Conjecture, which says that X contains no entire curves.
We prove that (a slightly strengthened version ...

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## Stably irrational hypersurfaces of small slopes Schreieder, Stefan | CIRM H

Multi angle

Research talks

We show that over any uncountable field of characteristic different from two, a very general hypersurface of dimension $n > 2$ and degree at least $log_2 (n) + 2$ is not stably rational. This significantly improves earlier results of Kollár and Totaro. As a byproduct of our proof, we obtain new counterexamples to the integral Hodge conjecture, answering a question of Voisin and Colliot-Thélène - Voisin.

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## Automorphisms of hyperkähler manifolds​ - Lecture 3 Sarti, Alessandra | CIRM H

Multi angle

Research talks;Algebraic and Complex Geometry

In the 80's Beauville generalized several foundational results of Nikulin on automorphism groups of K3 surfaces to hyperkähler manifolds. Since then the study of automorphism groups of hyperkähler manifolds and in particular of hyperkähler fourfolds got very much attention. I will present some classification results for automorphisms on hyperkähler fourfolds that are deformation equivalent to the Hilbert scheme of two points on a K3 surface and describe some explicit examples. I will give particular attention to double EPW sextics, that admit in a natural way a non-symplectic involution. Time permitting I will show how the rich geometry of double EPW sextics has an important connection to a classical question of U. Morin (1930). In the 80's Beauville generalized several foundational results of Nikulin on automorphism groups of K3 surfaces to hyperkähler manifolds. Since then the study of automorphism groups of hyperkähler manifolds and in particular of hyperkähler fourfolds got very much attention. I will present some classification results for automorphisms on hyperkähler fourfolds that are deformation equivalent to the Hilbert scheme of two points on a K3 surface and ...

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## Automorphisms of hyperkähler manifolds​ - Lecture 2 Sarti, Alessandra | CIRM H

Multi angle

Research talks;Algebraic and Complex Geometry

In the 80's Beauville generalized several foundational results of Nikulin on automorphism groups of K3 surfaces to hyperkähler manifolds. Since then the study of automorphism groups of hyperkähler manifolds and in particular of hyperkähler fourfolds got very much attention. I will present some classification results for automorphisms on hyperkähler fourfolds that are deformation equivalent to the Hilbert scheme of two points on a K3 surface and describe some explicit examples. I will give particular attention to double EPW sextics, that admit in a natural way a non-symplectic involution. Time permitting I will show how the rich geometry of double EPW sextics has an important connection to a classical question of U. Morin (1930). In the 80's Beauville generalized several foundational results of Nikulin on automorphism groups of K3 surfaces to hyperkähler manifolds. Since then the study of automorphism groups of hyperkähler manifolds and in particular of hyperkähler fourfolds got very much attention. I will present some classification results for automorphisms on hyperkähler fourfolds that are deformation equivalent to the Hilbert scheme of two points on a K3 surface and ...

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## Stable rationality - Lecture 3 Pirutka, Alena | CIRM H

Multi angle

Research talks;Algebraic and Complex Geometry

Let X be a smooth and projective complex algebraic variety. Several notions, describing how close X is to projective space, have been developed: X is rational if an open subset of X is isomorphic to an open of a projective space, X is stably rational if this property holds for a product of X with some projective space, and X is unirational if X is rationally dominated by a projective space. A classical Lüroth problem is to find unirational nonrational varieties. This problem remained open till 1970th, when three types of such examples were produced: cubic threefolds (Clemens and Griffiths), some quartic threefolds (Iskovskikh and Manin), and some conic bundles (Artin et Mumford). The last examples are even not stably rational. The stable rationality of the first two examples was not known.
In a recent work C. Voisin established that a double solid ramified along a very general quartic is not stably rational. Inspired by this work, we showed that many quartic solids are not stably rational (joint work with J.-L. Colliot-Thélène). More generally, B. Totaro showed that a very general hypersurface of degree d is not stably rational if d/2 is at least the smallest integer not smaller than (n+2)/3. The same method allowed us to show that the rationality is not a deformation invariant (joint with B. Hassett and Y. Tschinkel).
In this series of lectures, we will discuss the methods to obtain the results above: the universal properties of the Chow group of zero-cycles, the decomposition of the diagonal, and the specialization arguments.
Let X be a smooth and projective complex algebraic variety. Several notions, describing how close X is to projective space, have been developed: X is rational if an open subset of X is isomorphic to an open of a projective space, X is stably rational if this property holds for a product of X with some projective space, and X is unirational if X is rationally dominated by a projective space. A classical Lüroth problem is to find unirational ...

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## Bertini theorems in arithmetic geometry Charles, François | CIRM H

Multi angle

Research talks;Algebraic and Complex Geometry;Number Theory

The classical Bertini irreducibility theorem states that if $X$ is an irreducible projective variety of dimension at least 2 over an infinite field, then $X$ has an irreducible hyperplane section. The proof does not apply in arithmetic situations, where one wants to work over the integers or a finite fields. I will discuss how to amend the theorem in these cases (joint with Bjorn Poonen over finite fields).

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## Gonality and zero-cycles of abelian varieties Voisin, Claire | CIRM H

Multi angle

Research talks;Algebraic and Complex Geometry

The gonality of a variety is defined as the minimal gonality of curve sitting in the variety. We prove that the gonality of a very general abelian variety of dimension $g$ goes to infinity with $g$. We use for this a (straightforward) generalization of a method due to Pirola that we will describe. The method also leads to a number of other applications concerning $0$-cycles modulo rational equivalence on very general abelian varieties.

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## Birationally rigid Fano threefold hypersurfaces Cheltsov, Ivan ; Park, Jihun | American Mathematical Society 2016

Ouvrage

- v; 117 p.
ISBN 978-1-4704-2316-2

Memoirs of the american mathematical society , 1167

Localisation : Collection 1er étage

hypersurface de Fano # espace projectif pondéré # rigidité birationnelle # involution birationnelle

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## Lectures on curves, surfaces and projective varieties:a classical view of algebraic geometry Beltrametti, Mauro C. ; Carletti, Ettore ; Gallarati, Dionisio ; Monti Bragadin, Giacomo ; Sullivan, Francis | European Mathematical Society 2009

Ouvrage

- xv; 491 p.
ISBN 978-3-03719-064-7

EMS textbooks in mathematics

Localisation : Ouvrage RdC (LECT)

géométrie algébrique # correspondance birationnelle # courbe # variétés projectives # surface

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