Séminaire de géométrie algébrique

Le jeudi à 14h.
septembre-décembre ENS ou à distance, janvier-avril à distance ou Jussieu, mai-juin à distance ou Sophie Germain

45 rue d'Ulm, Paris 5è (salle W) ou 4 place Jussieu, Paris 5e ou Bat Sophie Germain, av de France
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Avril 2021 Affiche
01/04/2021 14h00 () à distance Georg Oberdieck,
Gromov-Witten theory and Noether-Lefschetz theory for holomorphic-symplectic varieties
396 751 8661,
Abstract: Maulik and Pandharipande proved a relation between three different theories associated to a 1-parameter family of smooth K3 surfaces:

(i) the Gromov-Witten invariants of the total space of the family in fiber classes
(ii) the Noether-Lefschetz numbers of the family
(iii) the (reduced) Gromov-Witten invariants of a fiber.

A similar version holds for any family of holomorphic-symplectic varieties. In this talk I will explain what shape this relation takes for K3[2]-type, and what it implies for Noether-Lefschetz numbers of Debarre-Voisin fourfolds. In particular, this leads to a new proof (and strengthening) of a result of Debarre, Han, O’Grady and Voisin on the existence of HLS divisors on the moduli of DV fourfolds.
08/04/2021 14h00 () à distance Irma Pallares Torres,
The Brasselet-Schürmann-Yokura conjecture on L-classes of singular varieties.
396 751 8661, Abstract: The Brasselet-Schürmann-Yokura conjecture predicts the equality between the Hodge L-class and the Goresky-MacPherson L-class for compact complex algebraic varieties that are rational homology manifolds. In this talk, we give two different proofs of this conjecture. The first proof is for projective varieties, and it is based on cubical hyperresolutions, the Decomposition Theorem, and classical Hodge theory. This is a joint work with J. Fernández de Bobadilla. The second proof is for general compact algebraic varieties by using the theory of mixed Hodge modules. This is a joint work with J. Fernández de Bobadilla and M. Saito.