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| 06/11/2025 | 14h00 (salle W, esc B 4ème étage) à l'ENS | ||||
| Abstract: Kodaira classified all possible singular fibers in minimal elliptic fibrations over a curve. Pushing it to higher dimensions, Matsushita (2001) classified all possible codimension 1 fibers in Lagrangian fibrations of relative dimension 2. Hwang-Oguiso (2009-2011) subsequently classified all possible characteristic cycles in codimension 1 fibers in arbitrary-dimensional Lagrangian fibrations. Such a result was used/enhanced in the recent work of Engel-Filipazzi-Greer-Mauri-Svaldi (2025) to bound certain Calabi-Yau varieties. In this talk, I will classify all possible singular fibers arising in certain arbitrary-dimensional abelian fibrations over a curve, both semistable and unstable, once again generalizing the work of Kodaira, Matsushita, and Hwang-Oguiso. | |||||
| 13/11/2025 | 14h00 (salle W, esc B 4ème étage) à l'ENS | ||||
| Les variétés hyperkählériennes sont des généralisations naturelles des surfaces K3 en dimension supérieure. Les descriptions des familles localement complètes de telles variétés sont connues dans très peu de cas. Dans cet exposé, je décrirai d'abord la géométrie projective du carré de Hilbert d'une surface K3 de genre 7 ou 8, en utilisant son modèle de Mukai : dans chaque cas, on retrouve un lieu de dégénérescence dans un espace homogène ambiant. J'en déduis ensuite une description géométrique pour les deux familles localement complètes de type K3^[2] (de carré 4 et 6 avec divisibilité 1), en termes de hypersurfaces de type Coble. Il s'agit d'un travail en commun avec Ángel Ríos Ortiz et Andrés Rojas, et un travail en cours aussi avec Benedetta Piroddi. | |||||
| 27/11/2025 | 14h00 (salle W, esc B 4ème étage) à l'ENS | ||||
| Abstract: Given a plane contained in a cubic fourfold, one can construct an associated K3 surface equipped with a Brauer class, such that the twisted derived category of the K3 surface is equivalent to the Kuznetsov component of the cubic fourfold. In this talk, we consider the case where the cubic fourfold contains (at least) two planes. There are three 18-dimensional families of such cubic fourfolds, depending on how the two planes intersect: They may be disjoint, meet at a point, or intersect along a line. In the first case, Voisin has shown that the associated K3 surfaces are isomorphic, but this is not true for generic members of the other two families. Motivated by this observation, we discuss the geometry, Hodge theory and derived categories of K3 surfaces associated to a cubic fourfold containing two planes intersecting along a line. In particular, we interpret the twisted derived equivalence of these K3 surfaces as an instance of a theorem of Donagi and Pantev. | |||||
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| 04/12/2025 | 14h00 (salle W, esc B 4ème étage) à l'ENS | ||||
| Abstract. A real function is totally real if the inverse image of any real value consists entirely of real points. Such a function gives an (unramified) covering of a real curve over the circle. Kummer and Shaw have introduced the "separating semigroup" of a real curve as all possible multidegrees appearing in this way. We overview what is known on this semigroup, paying a special attention to the elements of degree equal to the genus of the curve. Based on a joint work with Stepan Orevkov. | |||||
| 11/12/2025 | 14h00 (salle W, esc B 4ème étage) à l'ENS | ||||