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# Documents  Voisin, Claire | enregistrements trouvés : 12

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## Interview au CIRM : Claire Voisin Voisin, Claire | CIRM H

Post-edited

Outreach;Mathematics Education and Popularization of Mathematics

Claire Voisin, mathématicienne française, est Directrice de recherche au Centre national de la recherche scientifique (CNRS) à l'Institut de mathématiques de Jussieu, elle est membre de l'Académie des sciences et titulaire de la nouvelle chaire de mathématiques " géométrie algébrique " au Collège de France. Elle a reçu de nombreux prix nationaux et internationaux pour ses travaux en géométrie algébrique, et en particulier pour la résolution de la conjecture de Koidara sur les variétés de Kälher compactes et celle de la conjecture de Green sur les syzygies. Elle est depuis 2010 membre de l'Académie des sciences. Depuis le 2 juin 2016, elle est titulaire de la nouvelle chaire de mathématique " géométrie algébrique " devenant ainsi la première femme mathématicienne à entrer au Collège de France. Ses recherches portent sur la géométrie algébrique, notamment sur la conjecture de Hodge4, dans la lignée d'Alexandre Grothendieck ; la symétrie miroir et la géométrie complexe kählérienne.

Distinctions :

Médaille de bronze du CNRS (1988) puis médaille d'argent (2006)et médaille d'or (2016)
Prix IBM jeune chercheur (1989)
Prix EMS de la Société mathématique européenne (1992)
Prix Servant décerné par l'Académie des sciences (1996)
Prix Sophie-Germain décerné par l'Académie des sciences (2003)
Prix Ruth Lyttle Satter décerné par l'AMS (2007)
Clay Research Award en 2008
Prix Heinz Hopf (2015)
Officier de l'ordre national de la Légion d'honneur (2016)
Prix Shaw (2017)
Claire Voisin, mathématicienne française, est Directrice de recherche au Centre national de la recherche scientifique (CNRS) à l'Institut de mathématiques de Jussieu, elle est membre de l'Académie des sciences et titulaire de la nouvelle chaire de mathématiques " géométrie algébrique " au Collège de France. Elle a reçu de nombreux prix nationaux et internationaux pour ses travaux en géométrie algébrique, et en particulier pour la résolution de ...

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## Rationality of Fano 3-folds over non-closed fields Kuznetsov, Alexander | CIRM H

Post-edited

Algebraic and Complex Geometry

In the talk I will discuss rationality criteria for Fano 3-folds of geometric Picard number 1 over a non-closed field $k$ of characteristic 0. Among these there are 8 types of geometrically rational varieties. We prove that in one of these cases any variety of this type is k-rational, in four cases the criterion of rationality is the existence of a $k$-rational point, and in the last three cases the criterion is the existence of a $k$-rational point and a k rational curve of genus 0 and degree 1, 2, and 3 respectively. The last result is based on recent results of Benoist-Wittenberg. This is a joint work with Yuri Prokhorov. In the talk I will discuss rationality criteria for Fano 3-folds of geometric Picard number 1 over a non-closed field $k$ of characteristic 0. Among these there are 8 types of geometrically rational varieties. We prove that in one of these cases any variety of this type is k-rational, in four cases the criterion of rationality is the existence of a $k$-rational point, and in the last three cases the criterion is the existence of a $k$-rational ...

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

Multi angle

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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## Special rational fibrations in Fano 4-folds Casagrande, Cinzia | CIRM H

Multi angle

Algebraic and Complex Geometry

Smooth, complex Fano 4-folds are not classified, and we still lack a good understanding of their general properties. We focus on Fano 4-folds with large second Betti number $b_{2}$, studied via birational geometry and the detailed analysis of their contractions and rational contractions (we recall that a contraction is a morphism with connected fibers onto a normal projective variety, and a rational contraction is given by a sequence of flips followed by a contraction). The main result that we want to present is the following: let $X$ be a Fano 4-fold having a nonconstant rational contraction $X --> Y$ of fiber type. Then either $b_{2}(X)$ is at most 18, with equality only for a product of surfaces, or $Y$ is $\mathbb{P}^{1}$ or $\mathbb{P}^{2}$. The proof is achieved by reducing to the case of "special" rational contractions of fiber type. We will explain this notion and give an idea of the techniques that are used. Smooth, complex Fano 4-folds are not classified, and we still lack a good understanding of their general properties. We focus on Fano 4-folds with large second Betti number $b_{2}$, studied via birational geometry and the detailed analysis of their contractions and rational contractions (we recall that a contraction is a morphism with connected fibers onto a normal projective variety, and a rational contraction is given by a sequence of flips ...

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## Gushel-Mukai varieties and their periods Debarre, Olivier | CIRM H

Multi angle

Algebraic and Complex Geometry

Gushel-Mukai varieties are defined as the intersection of the Grassmannian Gr(2, 5) in its Plücker embedding, with a quadric and a linear space. They occur in dimension 6 (with a slighty modified construction), 5, 4, 3, 2 (where they are just K3 surfaces of degree 10), and 1 (where they are just genus 6 curves). Their theory parallels that of another important class of Fano varieties, cubic fourfolds, with many common features such as the presence of a canonically attached hyperkähler fourfold: the variety of lines for a cubic is replaced here with a double EPW sextic.
There is a big difference though: in dimension at least 3, GM varieties attached to a given EPW sextic form a family of positive dimension. However, we prove that the Hodge structure of any of these GM varieties can be reconstructed from that of the EPW sextic or of an associated surface of general type, depending on the parity of the dimension (for cubic fourfolds, the corresponding statement was proved in 1985 by Beauville and Donagi). This is joint work with Alexander Kuznetsov.
Gushel-Mukai varieties are defined as the intersection of the Grassmannian Gr(2, 5) in its Plücker embedding, with a quadric and a linear space. They occur in dimension 6 (with a slighty modified construction), 5, 4, 3, 2 (where they are just K3 surfaces of degree 10), and 1 (where they are just genus 6 curves). Their theory parallels that of another important class of Fano varieties, cubic fourfolds, with many common features such as the ...

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## Algebraic and arithmetic aspects of twistor spaces Huybrechts, Daniel | CIRM H

Multi angle

Algebraic and Complex Geometry

I will recall the well-known notion of twistor spaces for K3 surfaces (and Hyperkähler manifolds) and discuss some natural questions relating to the algebraic and arithmetic geometry of their fibres.

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## Cayley-Bacharach theorems with excess vanishing Lazarsfeld, Robert | CIRM H

Multi angle

A classical result usually attributed to Cayley and Bacharach asserts that if two plane curves of degrees c and d meet in cd points, then any curve of degree (c + d - 3) passing through all but one of these points must also pass through the remaining one. In the late 1970s, Griffiths and Harris showed that this is a special case of a general result about zero-loci of sections of a vector bundle. Inspired by a recent paper of Mu-Lin Li, I will describe a generalization allowing for excess vanishing. Multiplier ideals enter the picture in a natural way. Time permitting, I will also explain how a result due to Tan and Viehweg leads to statements of Cayley-Bacharach type for determinantal loci. This is joint work with Lawrence Ein. A classical result usually attributed to Cayley and Bacharach asserts that if two plane curves of degrees c and d meet in cd points, then any curve of degree (c + d - 3) passing through all but one of these points must also pass through the remaining one. In the late 1970s, Griffiths and Harris showed that this is a special case of a general result about zero-loci of sections of a vector bundle. Inspired by a recent paper of Mu-Lin Li, I will ...

14F05

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## Symétrie miroir Voisin, Claire | Société Mathématique de France 1996

Ouvrage

ISBN 978-2-85629-048-4

Panoramas et synthèses , 0002

Localisation : Collection 1er étage

cohomologie de Dolbeault # cohomologie quantique # conjecture de Gepner # construction de Givental # interprétation de Witten # origine physique # quantification # symétrie miroir # travaux de Batyrev # travaux de Candelas- de la Ossa-Green- Parkes # variété de Calabi Yau

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## Mirror symmetry Voisin, Claire ; Cooke, Roger | American Mathematical Society 1999

Ouvrage

ISBN 978-0-8218-1947-0

SMF/AMS texts and monographs , 0001

Localisation : Collection 1er étage

symétrie de miroir # théorie des champs quantiques # variété

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## Théorie de Hodge et géométrie algébrique complexe Voisin, Claire | Société Mathématique de France 2002

Ouvrage

- 595 p.
ISBN 978-2-85629-129-0

Cours spécialisés , 0010

Localisation : Collection 1er étage

cohomologie des faisceaux # métrique Kählérienne # structure de Hodge # complexe de Rham # suite spectrale # théorème de Lefschetz # connexion de Gauss-Manin # transversabilité # classe de cycles # correspondance

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## Hodge theory and complex algebraic geometry II Voisin, Claire ; Schneps, Leila | Cambridge University Press 2007

Ouvrage

- 351 p.
ISBN 978-0-521-80283-0

Cambridge studies in advanced mathematics , 0077

Localisation : Ouvrage RdC (VOIS)

géométrie algébrique # méthode transcendentale # cycles algébriques # matrices périodiques # groupe de choix # théorie de Hodge # conjecture de Bloch-Beilinson # théorème de Torelli

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## Hodge theory and complex algebraic geometry I Voisin, Claire ; Schneps, Leila | Cambridge University Press 2007

Ouvrage

- 322 p.
ISBN 978-0-521-71801-1

Cambridge studies in advanced mathematics , 0076

Localisation : Ouvrage RdC (VOIS)

géométrie algébrique # méthodes transcendantales # cycle algébrique # variation de structure de Hodge # matrices périodiques # géométrie Kälherienne # décomposition de Lefschetz

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Titres de périodiques et e-books électroniques (Depuis le CIRM)

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