Moduli of abelian surfaces, symmetric theta structures and theta\n characteristics

2014/09/17 by Michele Bolognesi, Alex Massarenti, Bolognesi, Michele +1
Mathematics · #11G10 #11G15 #14E05 #14E08 #14K10 (Primary) #14M20 (Secondary) #Advanced Algebra and Geometry #Advanced Mathematical Identities #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics

paper · pdf · doi:10.48550/arxiv.1409.5033

openalex publication_date 2014/09/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We study the birational geometry of some moduli spaces of abelian varieties\nwith extra structure: in particular, with a symmetric theta structure and an\nodd theta characteristic. For a (d₁,d₂)-polarized abelian surface, we show\nhow the parities of the d_i influence the relation between canonical level\nstructures and symmetric theta structures. For certain values of d₁ and\nd₂, a theta characteristic is needed in order to define Theta-null maps. We\nuse these Theta-null maps and preceding work of other authors on the\nrepresentations of the Heisenberg group to study the birational geometry and\nthe Kodaira dimension of these moduli spaces.\n

Citations

• On the unirationality of 3-fold conic bundles
• The moduli space of (1,11)-polarized abelian surfaces is unirational

Related

• The Kodaira dimension of certain moduli spaces of abelian surfaces
• Calabi-Yau Threefolds and Moduli of Abelian Surfaces I
• The moduli space of (1,11)-polarized abelian surfaces is unirational
• Moduli of (1,7)-polarized abelian surfaces via syzygies
• The moduli space of bilevel-6 abelian surfaces