PhD course: Stable bundles on hyper-Kähler manifolds
Wednesday 15-17, aula B (Dipartimento di Matematica "Guido Castelnuovo")
Sapienza Università di Roma
October 9--30, 2024
The aim of this course is to present some recent advances in the
theory of stable sheaves on higher dimensional hyper-Kähler manifolds.
In the first part we will review Mukai's theory on K3 surfaces.
We will then consider hyper-Kähler fourfolds, by presenting in
this setting general results due to O'Grady, Markman, Beckmann, and Bottini.
Some references:
(introduction to stability of sheaves)
J. Le Potier, Lectures on Vector Bundles, Cambridge 1997
D. Huybrechts, M. Lehn, The Geometry of Moduli Spaces of Sheaves,
Cambridge 2010
(K3 surfaces)
D. Huybrechts, Lectures on K3 surfaces, Cambridge 2016
S. Mukai, On the moduli space of bundles on K3 surfaces, I, Tata
Lectures (1987)
(hyper-Kähler manifolds)
K. O'Grady, Modular sheaves on hyperkähler varieties, Algebraic
Geometry (2022)
E. Markman, Stable vector bundles on a hyper-Kähler manifold with
a rank 1 obstruction map are modular, Kyoto Math J (2023)
T. Beckmann, Atomic objects on hyper-Kähler manifolds, preprint (2022)
A. Bottini, Towards a modular construction of OG10, Compositio
(2024)