Séminaire Arithmétique et géométrie algébrique
organisé par l'équipe Arithmétique et géométrie algébrique
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Alessio Bottini
The period-index problem for hyper-Kähler varieties
5 mars 2026 - 14:00Salle de séminaires IRMA
The period-index conjecture is a fundamental problem concerning the Brauer group of algebraic varieties. For hyper-Kähler varieties, whose (birational) geometry is controlled by the second cohomology, it is expected that a stronger form of this conjecture holds. In this talk, I will present joint work with Daniel Huybrechts that provides new evidence for this expectation.
Following a brief introduction to the problem, I will discuss a proof of a variant of the conjecture where the classical index is replaced by a Hodge-theoretic one. Then, I will explain how to verify the conjecture for most Brauer classes on hyper-Kähler varieties of K3n-type. -
Enrico Fatighenti
Modular vector bundles on hyperkähler manifolds
12 mars 2026 - 14:00Salle de séminaires IRMA
We exhibit examples of slope-stable and modular vector bundles on a hyperkähler manifold of K3^[2]-type. These are obtained by performing standard linear algebra constructions on the examples studied by O’Grady of (rigid) modular bundles on the Fano varieties of lines of a general cubic 4-fold and the Debarre-Voisin hyperkähler. Interestingly enough, these constructions are almost never infinitesimally rigid, and more precisely we show how to get (infinitely many) 20 and 40 dimensional families. This is a joint work with Claudio Onorati. Time permitting, I will also present a joint work with Alessandro D'Andrea and Claudio Onorati on a connection between discriminants of vector bundles on smooth and projective varieties and representation theory of GL(n). -
Cécile Gachet
tbd
19 mars 2026 - 14:00Salle de séminaires IRMA
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Andrea Gallese
tbd
2 avril 2026 - 14:00Salle de séminaires IRMA
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German Stefanich
tbd
9 avril 2026 - 14:00Salle de séminaires IRMA