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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 ...

14J50 ; 14J28 ; 14J35 ; 14J70 ; 14M15 ; 14N20

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Research talks;Algebraic and Complex Geometry

Hyperkähler manifolds are higher-dimensional analogs of K3 surfaces. Verbitsky and Markmann recently proved that their period map is an open embedding. In a joint work with E. Macri, we explicitly determine the image of this map in some cases. I will explain this result together with a nice application (found by Bayer and Mongardi) to the (almost complete) determination of the image of the period map for cubic fourfolds, hereby partially recovering a result of Laza. Hyperkähler manifolds are higher-dimensional analogs of K3 surfaces. Verbitsky and Markmann recently proved that their period map is an open embedding. In a joint work with E. Macri, we explicitly determine the image of this map in some cases. I will explain this result together with a nice application (found by Bayer and Mongardi) to the (almost complete) determination of the image of the period map for cubic fourfolds, hereby partially ...

14C34 ; 14E07 ; 14J50 ; 14J60

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Research schools

Aim of the lecture is to give an introduction to $K3$ surfaces, that are special algebraic surfaces with an extremely rich geometry. The most easy example of such a surface is the Fermat quartic in complex three-dimensional space.
The name $K3$ was given by André Weil in 1958 in honour of the three remarkable mathematicians: Kummer, Kähler and Kodaira and of the beautiful K2 mountain at Cachemire.
The topics of the lecture are the following:

* $K3$ surfaces in the Enriques-Kodaira classification.
* Examples; Kummer surfaces.
* Basic properties of $K3$ surfaces; Torelli theorem and surjectivity of the period map.
* The study of automorphisms on $K3$ surfaces: basic facts, examples.
* Symplectic automorphisms of $K3$ surfaces, classification, moduli spaces.
Aim of the lecture is to give an introduction to $K3$ surfaces, that are special algebraic surfaces with an extremely rich geometry. The most easy example of such a surface is the Fermat quartic in complex three-dimensional space.
The name $K3$ was given by André Weil in 1958 in honour of the three remarkable mathematicians: Kummer, Kähler and Kodaira and of the beautiful K2 mountain at Cachemire.
The topics of the lecture are the following:

* ...

14J10 ; 14J28 ; 14J50 ; 14C20 ; 14C22 ; 14J27 ; 14L30

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- 276 p.
ISBN 978-0-8218-3476-3

Contemporary mathematics , 0369

Localisation : Collection 1er étage

géométrie algébrique # géométrie affine # conjecture jacobienne # automorphisme de surface # application rationnelle # idéal polynomial

14RXX ; 14H50 ; 14J50 ; 14E05 ; 13P10 ; 12Y05

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- 239 p.
ISBN 978-0-8218-4201-0

Contemporary mathematics , 0422

Localisation : Collection 1er étage

géométrie algébrique # Igor Dolgachev # courbe # surface algébrique # espace de module # forme automorphe # treillis de Mordell-Weil # variété de Kähler

11D25 ; 11F11 ; 14H10 ; 14J15 ; 14J26 ; 14J28 ; 14J50 ; 14J60 ; 32N15

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- 382 p.
ISBN 978-4-931469-63-1

Advanced studies in pure mathematics , 0060

Localisation : Collection 1er étage

géométrie algébrique # géométrie biratinnelle # surface # variétés symplectiques # cohomologie quantique

14-06 ; 14E07 ; 14J27 ; 06B05 ; 11G05 ; 11G07 ; 11G50 ; 14J20 ; 14J50 ; 14E30 ; 14E05 ; 14E25 ; 14L15 ; 14J17 ; 14J29 ; 14J10 ; 53D05 ; 14N35 ; 53D45 ; 14J26 ; 14J28 ; 14H50 ; 14E20 ; 14J60

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- 474 p.
ISBN 978-4-86497-048-8

Advanced studies in pure mathematics , 0075

Localisation : Collection 1er étage

géométrie algébrique # groupe d'automorphisme # groupe algébrique # variété algébrique # automorphisme birationnel

14-06 ; 14R20 ; 14R10 ; 14E07 ; 14J26 ; 05E18 ; 14E05 ; 14E30 ; 14J10 ; 14J45 ; 14M17 ; 14M25 ; 13A50 ; 14D07 ; 14H50 ; 14J50 ; 14L10 ; 14L30 ; 14R05 ; 14R25 ; 20E06 ; 20F55 ; 32G20 ; 32M12 ; 52B20

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- 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 ...

11S15 ; 13D10 ; 14-02 ; 14B05 ; 14B12 ; 14C17 ; 14C20 ; 14C35 ; 14D06 ; 14D15 ; 14D20 ; 14E15 ; 14E30 ; 14F43 ; 14H10 ; 14H40 ; 14H42 ; 14J17 ; 14J28 ; 14J30 ; 14J32 ; 14J50 ; 14J70 ; 14K10 ; 14K25 ; 14L30 ; 14M15 ; 14M17 ; 14M25 ; 14N10 ; 14N15 ; 32G10 ; 32Q45 ; 34A30 ; 53D05 ; 55N91 ; 01-02 ; 01A70 ; 05E05 ; 11S85 ; 13A35 ; 14B10 ; 14C30 ; 14F18 ; 14J26 ; 14N20 ; 19D55 ; 32S25 ; 53D20 ; 57R45

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- 537 p.
ISBN 978-4-86497-032-7

Advanced studies in pure mathematics , 0069

Localisation : Collection 1er étage

théorie des modules # géométrie algébrique

14-06 ; 11G50 ; 14C05 ; 14C22 ; 14C25 ; 14C30 ; 14D20 ; 14D21 ; 14D23 ; 14H10 ; 14H50 ; 14J10 ; 14J15 ; 14J26 ; 14J27 ; 14J28 ; 14J29 ; 14J50 ; 14J60 ; 14K10 ; 14K25 ; 14N35 ; 18E30 ; 32M15 ; 32N15

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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 ...

14J50 ; 14J28 ; 14J35 ; 14J70 ; 14M15 ; 14N20

... Lire [+]

Déposez votre fichier ici pour le déplacer vers cet enregistrement.

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 ...

14J50 ; 14J28 ; 14J35 ; 14J70 ; 14M15 ; 14N20

... Lire [+]

Déposez votre fichier ici pour le déplacer vers cet enregistrement.

Research schools

Aim of the lecture is to give an introduction to $K3$ surfaces, that are special algebraic surfaces with an extremely rich geometry. The most easy example of such a surface is the Fermat quartic in complex three-dimensional space.
The name $K3$ was given by André Weil in 1958 in honour of the three remarkable mathematicians: Kummer, Kähler and Kodaira and of the beautiful K2 mountain at Cachemire.
The topics of the lecture are the following:

* $K3$ surfaces in the Enriques-Kodaira classification.
* Examples; Kummer surfaces.
* Basic properties of $K3$ surfaces; Torelli theorem and surjectivity of the period map.
* The study of automorphisms on $K3$ surfaces: basic facts, examples.
* Symplectic automorphisms of $K3$ surfaces, classification, moduli spaces.
Aim of the lecture is to give an introduction to $K3$ surfaces, that are special algebraic surfaces with an extremely rich geometry. The most easy example of such a surface is the Fermat quartic in complex three-dimensional space.
The name $K3$ was given by André Weil in 1958 in honour of the three remarkable mathematicians: Kummer, Kähler and Kodaira and of the beautiful K2 mountain at Cachemire.
The topics of the lecture are the following:

* ...

14J10 ; 14J28 ; 14J50 ; 14C20 ; 14C22 ; 14J27 ; 14L30

... Lire [+]

Déposez votre fichier ici pour le déplacer vers cet enregistrement.

Research schools

Aim of the lecture is to give an introduction to $K3$ surfaces, that are special algebraic surfaces with an extremely rich geometry. The most easy example of such a surface is the Fermat quartic in complex three-dimensional space.
The name $K3$ was given by André Weil in 1958 in honour of the three remarkable mathematicians: Kummer, Kähler and Kodaira and of the beautiful K2 mountain at Cachemire.
The topics of the lecture are the following:

* $K3$ surfaces in the Enriques-Kodaira classification.
* Examples; Kummer surfaces.
* Basic properties of $K3$ surfaces; Torelli theorem and surjectivity of the period map.
* The study of automorphisms on $K3$ surfaces: basic facts, examples.
* Symplectic automorphisms of $K3$ surfaces, classification, moduli spaces.
Aim of the lecture is to give an introduction to $K3$ surfaces, that are special algebraic surfaces with an extremely rich geometry. The most easy example of such a surface is the Fermat quartic in complex three-dimensional space.
The name $K3$ was given by André Weil in 1958 in honour of the three remarkable mathematicians: Kummer, Kähler and Kodaira and of the beautiful K2 mountain at Cachemire.
The topics of the lecture are the following:

* ...

14J10 ; 14J28 ; 14J50 ; 14C20 ; 14C22 ; 14J27 ; 14L30

... Lire [+]

Déposez votre fichier ici pour le déplacer vers cet enregistrement.

Research schools

Aim of the lecture is to give an introduction to $K3$ surfaces, that are special algebraic surfaces with an extremely rich geometry. The most easy example of such a surface is the Fermat quartic in complex three-dimensional space.
The name $K3$ was given by André Weil in 1958 in honour of the three remarkable mathematicians: Kummer, Kähler and Kodaira and of the beautiful K2 mountain at Cachemire.
The topics of the lecture are the following:

* $K3$ surfaces in the Enriques-Kodaira classification.
* Examples; Kummer surfaces.
* Basic properties of $K3$ surfaces; Torelli theorem and surjectivity of the period map.
* The study of automorphisms on $K3$ surfaces: basic facts, examples.
* Symplectic automorphisms of $K3$ surfaces, classification, moduli spaces.
Aim of the lecture is to give an introduction to $K3$ surfaces, that are special algebraic surfaces with an extremely rich geometry. The most easy example of such a surface is the Fermat quartic in complex three-dimensional space.
The name $K3$ was given by André Weil in 1958 in honour of the three remarkable mathematicians: Kummer, Kähler and Kodaira and of the beautiful K2 mountain at Cachemire.
The topics of the lecture are the following:

* ...

14J10 ; 14J28 ; 14J50 ; 14C20 ; 14C22 ; 14J27 ; 14L30

... Lire [+]

Déposez votre fichier ici pour le déplacer vers cet enregistrement.

Research schools

Aim of the lecture is to give an introduction to $K3$ surfaces, that are special algebraic surfaces with an extremely rich geometry. The most easy example of such a surface is the Fermat quartic in complex three-dimensional space.
The name $K3$ was given by André Weil in 1958 in honour of the three remarkable mathematicians: Kummer, Kähler and Kodaira and of the beautiful K2 mountain at Cachemire.
The topics of the lecture are the following:

* $K3$ surfaces in the Enriques-Kodaira classification.
* Examples; Kummer surfaces.
* Basic properties of $K3$ surfaces; Torelli theorem and surjectivity of the period map.
* The study of automorphisms on $K3$ surfaces: basic facts, examples.
* Symplectic automorphisms of $K3$ surfaces, classification, moduli spaces.
Aim of the lecture is to give an introduction to $K3$ surfaces, that are special algebraic surfaces with an extremely rich geometry. The most easy example of such a surface is the Fermat quartic in complex three-dimensional space.
The name $K3$ was given by André Weil in 1958 in honour of the three remarkable mathematicians: Kummer, Kähler and Kodaira and of the beautiful K2 mountain at Cachemire.
The topics of the lecture are the following:

* ...

14J10 ; 14J28 ; 14J50 ; 14C20 ; 14C22 ; 14J27 ; 14L30

... Lire [+]

Déposez votre fichier ici pour le déplacer vers cet enregistrement.

Research schools

Aim of the lecture is to give an introduction to $K3$ surfaces, that are special algebraic surfaces with an extremely rich geometry. The most easy example of such a surface is the Fermat quartic in complex three-dimensional space.
The name $K3$ was given by André Weil in 1958 in honour of the three remarkable mathematicians: Kummer, Kähler and Kodaira and of the beautiful K2 mountain at Cachemire.
The topics of the lecture are the following:

* $K3$ surfaces in the Enriques-Kodaira classification.
* Examples; Kummer surfaces.
* Basic properties of $K3$ surfaces; Torelli theorem and surjectivity of the period map.
* The study of automorphisms on $K3$ surfaces: basic facts, examples.
* Symplectic automorphisms of $K3$ surfaces, classification, moduli spaces.
Aim of the lecture is to give an introduction to $K3$ surfaces, that are special algebraic surfaces with an extremely rich geometry. The most easy example of such a surface is the Fermat quartic in complex three-dimensional space.
The name $K3$ was given by André Weil in 1958 in honour of the three remarkable mathematicians: Kummer, Kähler and Kodaira and of the beautiful K2 mountain at Cachemire.
The topics of the lecture are the following:

* ...

14J10 ; 14J28 ; 14J50 ; 14C20 ; 14C22 ; 14J27 ; 14L30

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- ix; 399 p.
ISBN 978-3-319-29958-7

Progress in mathematics , 0315

Localisation : Collection 1er étage

géométrie algébrique # module des surface K3 # théorie des treillis # système dynamique # théorie des nombres # conjecture de Tate # théorie des cordes # variété symplectique holomorphe

14J28 ; 14J15 ; 14J10 ; 14J32 ; 14J33 ; 14J50 ; 14N35

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- x; 341 p.
ISBN 978-2-85629-338-6

Panoramas et synthèses , 0030

Localisation : Collection 1er étage

Dynamique holomorphe # système dynamique algébrique # géométrie algébrique # géométrie diophantienne # théorie du potentiel # hauteurs # équidistribution # théorie ergodique

14E07 ; 14J50 ; 32H50 ; 11-02 ; 11G50 ; 14K15 ; 37F10

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- xx; 207 p.
ISBN 978-0-8176-4874-9

Progress in mathematics , 0278

Localisation : Collection 1er étage

géométrie algébrique # action de groupe # théorie des invariants modulaires

12Exx ; 13A50 ; 14J50 ; 14L24 ; 14L30 ; 14M17 ; 14R25 ; 14R10 ; 16S32 ; 17B45 ; 20Cxx ; 20G05 ; 20G20 ; 20H15 ; 22E15 ; 22E46 ; 32M05 ; 53C55 ; 53C35 ; 53D20 ; 14-06 ; 13-06

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