Two days on hyper-Kähler varieties and related topics

The workshop will take place from Thursday morning, June 25, to Friday noon, June 26, 2026.

Schedule

Thursday 25 June

9:30 - 10:30  Matteo Verni

Coffee break

11:00 - 12:00 Xiaolei Zhao

Lunch

14:00 - 15:00 Calla Tschanz

Coffee break

15:30 - 16:30 Howard Nuer

Friday 26 June

9:30 - 10:30 Andrés Rojas

Coffee break

11:00 - 12:00 Daniele Agostini

Lunch

Abstracts

• Daniele Agostini

• Howard Nuer

• Andrés Rojas
  Title: Coble type hypersurfaces and hyperkähler fourfolds
  Abstract: A classical result, already observed by Coble, asserts that a genus 2 Jacobian (resp. the Kummer of a genus 3 Jacobian) can be embedded in \mathbb{P}^8 (resp. in \mathbb{P}^7) as the singular locus of a unique cubic (resp. quartic) hypersurface. We present a precise analogue of this result in the context of hyperkähler fourfolds, and discuss applications to the geometry of two moduli spaces of polarized hyperkähler fourfolds of K3-type. This is a joint work with Benedetta Piroddi, Ángel Ríos, and Jieao Song.

• Calla Tschanz

• Matteo Verni
  Title: The Brauer group of Known Enriques manifolds
  Abstract: Enriques manifolds are the higher dimensional analogue of Enriques surfaces. Their study is similar, where the role played by K3 surfaces in dimension two is played by hyper-kähler manifolds in higher dimension. In this talk, we interest ourselves in the Brauer group of Enriques manifolds. This group is isomorphic to Z/2Z for Enriques surfaces. We explain how to compute it in the known higher dimensional examples, by purely topological means: this is closely related to the problem of computing H^3(X,Z)_tors of hyper-Kähler manifolds. We then describe  generalization in higher dimension of a result of Beauville, characterizing those Enriques surfaces for which the pullback of the nontrivial Brauer class vanishes, in terms of the existence of a special line bundle on its associated hyper-Kähler. For any Enriques manifold for which such a line bundle exists, we construct explicit trivial Brauer-Severi varieties on the hyper-Kähler which descend to nontrivial ones on the Enriques manifold. This is joint work with A. Frassineti, F. Rizzo and F. Tufo.

• Xiaolei Zhao

Venue

Bâtiment Sophie Germain, Université Paris Cité