Lecturers

• Alessandra Sarti, Université de Poitiers (France).

• Samuel Boissière, Université de Poitiers (France).

• Chiara Camere, Università degli Studi di Milano (Italy). 

• Paola Comparin, Universidad de la Frontera (Chile).

Description

The main object of the school will be irreducible holomorphic symplectic (IHS) manifolds. These manifolds have received a lot of interest in the last years since by a theorem of Beauville-Bogomolov, together with Calabi-Yau manifolds and tori they are the building blocks of all compact complex Kähler manifolds with zero first Chern class. Together with Calabi-Yau manifolds they can be seen as a higher dimensional generalisations of K3 surfaces and they share several interesting properties with them. One of the most important property is certainly the generalization by Markman and Verbitsky of the Torelli theorem. It is then natural to include in the school a part devoted to the geometry of K3 surfaces. A tentative list of topics could be the following:

• automorphism groups of K3 surfaces: the symplectic and non-symplectic automorphisms;

• elliptic fibrations on K3 surfaces;

• lattice theory and classification of the automorphism groups;

• introduction to IHS manifolds;

• automorphism groups of IHS manifolds: what does it change with respect to the case of the K3 surfaces?

• classification of finite automorphism groups acting on IHS manifolds;

• construction of the moduli spaces: the ball quotients.

A part of the school could be also devoted to some special topics as to explain the recent relation between K3 surfaces and finite complex reflection groups in particular it would be interesting to introduce the Lehrer-Springer theory or to introduce the use of the Smith theory in the study of automorphisms. The latter are powerful tools in the study of group actions on K3 surfaces respectively on IHS manifolds.

The school should be accessible to PhD students and to young researchers with basic knowledges in algebraic geometry and in the geometry of algebraic surfaces. The aim of the school is from one side to give an introduction to the subject and from the other side to provide general tools that are useful in the study of IHS manifolds.

Organizers

Elisa Postinghel (Trento), Luis Solá Conde (Trento)

Contact us at: singtn.math@unitn.it

Registration

Registration to the event in now closed.

Supported by

CIRM-FBK, Università di Trento, PRIN 2022 project " Birational geometry of moduli spaces and special varieties” prot. n. 20223B5S8L_002, Foundation Composition Mathematica, INdAM-GNSAGA