Séminaire de géométrie algébrique

Le jeudi à 14h.
septembre-décembre ENS, janvier-mars Jussieu, 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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Novembre 2019 Affiche

21/11/2019 14h (40+30) (salle W, esc B 4ème étage) ENS Frank Gounelas, Munich
Curves on K3 surfaces
Abstract: Bogomolov and Mumford proved that every complex projective K3 surface contains a rational curve. Since then, a lot of progress has been made by Bogomolov, Chen, Hassett, Li, Liedtke, Tschinkel and others, towards the stronger statement that any such surface in fact contains infinitely many rational curves. In this talk I will present joint work with Xi Chen and Christian Liedtke completing the remaining cases of this conjecture, reproving some of the main previously known cases more conceptually and extending the result to arbitrary genus.

Decembre 2019 Affiche

05/12/2019 14h (40+30) (salle W, esc B 4ème étage) ENS Johannes Schmitt,
Zero cycles on moduli spaces of curves
bstract: Tautological zero cycles form a one-dimensional subspace of the set of all algebraic zero-cycles on the moduli space of stable curves. The full group of zero cycles can in general be infinite-dimensional, so not all points of the moduli space will represent a tautological class. In the talk, I will present geometric conditions ensuring that a pointed curve does define a tautological point. On the other hand, given any point Q in the moduli space we can find other points P_1, ..., P_m such that Q+P_1+ ... + P_m is tautological. The necessary number m is uniformly bounded in terms of g,n, but the question of its minimal value is open. This is joint work with Rahul Pandharipande.