Séminaire de géométrie algébrique

Le jeudi à 14h.
septembre-décembre ENS, janvier-avril Jussieu, 25 avril-juin 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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Mars 2024 Affiche

28/03/2024 14h00 (5-02) Jussieu 15-25 Radu Laza,
Remarks on Calabi-Yau degenerations
L'exposé sera aussi diffusé par ZOOM:870 3083 2332, demander le mot de passe à Olivier Benoist, Olivier Debarre ou Frederic Han, ou inscrivez vous sur la liste de diffusion
it is a question of great interest to construct meaningful compactifications for the moduli of algebraic varieties of a specified type. For varieties of general type, and Fano type a fairly complete understanding of the compactification problem was obtained recently via the KSBA theory and respectively K-theory. The remaining case, that of K-trivial varieties turns out to be particularly challenging and the same time very interesting. After reviewing what we know in this case (especially new results, due to Alexeev-Engel for K3 surfaces), I will propose a canonical minimal compactification for the K-trivial case and discuss some evidence towards it. (Versions of this conjecture previously occur in work of Ambro/Fujino/Shokurov, Odaka, and respectively GGLR)
The point of view taken here is that of Hodge theory.
The talk is based on some joint work with R. Friedman. It is also closely related to joint work with Kollár, Saccà, Voisin [KLSV18] and respectively Green, Griffiths, and Robles [GGLR20].
28/03/2024 16h00 (15-16 413) Jussieu David Holmes,
The locus where a line bundle is trivial
L'exposé sera aussi diffusé par ZOOM:870 3083 2332, demander le mot de passe à Olivier Benoist, Olivier Debarre ou Frederic Han, ou inscrivez vous sur la liste de diffusion
Abstract: Given a line bundle L on a family of curves C, smooth and proper over a base scheme S, it is natural to study the locus of points of S where L is trivial. When one tries to extend to a family of stable curves, this ends up naturally yielding a cycle, not on S itself, but rather on a (log) blowup of S. One can choose to push down to S, but for some purposes the cycle on the blowup is the more fundamental object. I will describe two ways to compute the resulting class, known as the logarithmic double ramification cycle. This is joint work with Alessandro Chiodo

Avril 2024 Affiche

04/04/2024 14h00 (5-02) Jussieu 15-25 Yuji Odaka,
(à préciser)
L'exposé sera aussi diffusé par ZOOM:870 3083 2332, demander le mot de passe à Olivier Benoist, Olivier Debarre ou Frederic Han, ou inscrivez vous sur la liste de diffusion

25/04/2024 14h00 (1016) Bat. S. Germain Tiago Duarte-Guerreiro,
Examples of Mori Dream spaces of Picard rank 2 and their birational geometry
L'exposé sera aussi diffusé par ZOOM:870 3083 2332, demander le mot de passe à Olivier Benoist, Olivier Debarre ou Frederic Han, ou inscrivez vous sur la liste de diffusion
Abstract: Let X be an n-dimensional smooth projective Fano hypersurface, where n is at least 3. Suppose X contains Z, a k-dimensional smooth projective hypersurface in P^{k+1}, where k is at least 1. We give a constructive proof that Y - the blowup of X along Z - is a Mori dream space. In particular, we describe its Mori chamber decomposition and the associated birational models of Y. This is joint work with L. Campo and E. Paemurru.

Mai 2024 Affiche

02/05/2024 14h00 (1016) Bat. S. Germain Yueqiao Wu,
K-semistability of log Fano cone singularities
L'exposé sera aussi diffusé par ZOOM:870 3083 2332, demander le mot de passe à Olivier Benoist, Olivier Debarre ou Frederic Han, ou inscrivez vous sur la liste de diffusion
Abstract: K-stability of log Fano cone singularities was introduced by Collins-Sz\’ekelyhidi to serve as a local analog of K-stability of Fano varieties. In the Fano case, the result of Li-Xu states that to test K-stability, it suffices to test the so-called special test configurations. In this talk, I will talk about a local version of this result for log Fano cones. Our method relies on a non-Archimedean characterization of local K-stability.
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