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 are 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 these 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. For this reason it is natural to include in the school a part devoted to the geometry of K3 surfaces. 

The topics that will be studied in the school include:

• introduction to K3 surfaces,

• 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, description of the known examples,

• 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 manifold,

• construction of the moduli spaces.

The final part of the school will be devoted to recent progress on these topics : classification of K3 surfaces and IHS manifolds with big or special automorphism group, Enriques manifolds and the Morrison-Kawamata cone conjecture, Nikulin orbifolds, Singular sympletic varieties.

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 several general tools that are useful in the study of questions on IHS manifolds.

Equality and diversity

The organizers are committed to promote gender equality and to value diversity in academia. For this reason we will make reasonable attempts to secure a diverse line-up of speakers and participants in the series of Trento Schools in Geometry.

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