Moduli of abelian surfaces, symmetric theta structures and theta characteristics

  • Michele Bolognesi

    Université de Montpellier, France
  • Alex Massarenti

    Universidade Federal Fluminense - UFF, Niterói, Brazil

Abstract

We study the birational geometry of some moduli spaces of abelian varieties with extra structure: in particular, with a symmetric theta structure and an odd theta characteristic. For a ()-polarized abelian surface, we show how the parities of the influence the relation between canonical level structures and symmetric theta structures. For certain values of and , a theta characteristic is needed in order to define Theta-null maps. We use these Theta-null maps and preceding work of other authors on the representations of the Heisenberg group to study the birational geometry and the Kodaira dimension of these moduli spaces.

Cite this article

Michele Bolognesi, Alex Massarenti, Moduli of abelian surfaces, symmetric theta structures and theta characteristics. Comment. Math. Helv. 91 (2016), no. 3, pp. 563–608

DOI 10.4171/CMH/396