Modular Forms and Geometry of Modular Varieties

IMPA, Rio de Janeiro, May 4-8, 2015.

Many moduli spaces in algebraic geometry can be constructed as quotients of homogeneous domains by arithmetic groups. Among the best known examples are the moduli spaces of principally polarized Abelian varieties or of polarized K3 surfaces. The existence of automorphic forms with special properties often encodes much information about the geometry of the moduli spaces. For example special automorphic forms can often be used to determine whether certain moduli spaces are of general type or have negative Kodaira dimension. For the construction of forms with special properties, Borcherds modular forms play an essential role. At the same time automorphic forms can be often used to describe the Picard group of moduli spaces or, more generally, modular varieties. In this activity we want to explore some of the interactions between modular forms and the geometry of modular varieties.

Confirmed Specialists taking part of this concentration period are:

  • Klaus Hulek (Leibniz U. Hannover)
  • Shouhei Ma (Tokyo Inst. Techonology)
  • Giovanni Mongardi (U. Milano)
  • Riccardo Salvati Manni (U. Roma La Sapienza)
  • Gregory Sankaran (U. Bath)
  • Benjamin Wieneck (Leibniz U. Hannover)
  • Kenichi Yoshikawa (Kyoto U.)
Playlist Youtube:


Monday, May 4

Fundamental groups of toroidal compactifications - G.K. Sankaran

Moduli of polarized Enriques surfaces - K. Hulek

Tuesday, May 5

Analytic torsion invariant for K3 surfaces with involution - K.-I. Yoshikawa

Wednesday, May 6

The monodromy group of generalized Kummer varieties - G. Mongardi

Polarization types of Lagrangian fibrations - B. Wieneck

Thursday, May 7

Finiteness of 2-reflective lattices of signature (2,n) - S. Ma

A simple vector valued modular form with applications in algebraic geometry and modular forms - R. Salvati-Manni