Moduli of polarized Enriques surfaces

2015/02/09 by Valery Gritsenko, Klaus Hulek, Gritsenko, Valery +1
Computer Science · Mathematics · #Advanced Differential Equations and Dynamical Systems #Algebraic Geometry and Number Theory #Coding theory and cryptography #math.AG #msc:11F23 #msc:14D20 #msc:14G35 #msc:14J28

paper · pdf · doi:10.48550/arxiv.1502.02723

Main result slightly strengthened, minor corrections, improved presentation

arxiv created 2015/03/20 · arxiv updated 2015/03/23

Abstract

In this paper we consider moduli spaces of polarized and numerically polarized Enriques surfaces. The moduli spaces of numerically polarized Enriques surfaces can be described as open subsets of orthogonal modular varieties of dimension 10. One of the consequences of our description is that there are only finitely many isomorphism classes of moduli spaces of polarized and numerically polarized Enriques surfaces. We use modular forms to prove for a number of small degrees that the Kodaira dimension of the moduli space of numerically polarized Enriques surfaces is negative. Finally we prove that there are infinitely many polarizatons for which the moduli space of numerically polarized Enriques surfaces is birational to the moduli space of unpolarized Enriques surfaces with a level 2 structure.

Related

• Compact moduli of Enriques surfaces with a numerical polarization of degree 2
• On moduli spaces of polarized Enriques surfaces
• Cohomology of the moduli space of degree two Enriques surfaces
• Simple isotropic decompositions of the curve sections of the known\n Enriques-Fano threefolds
• The moduli space of (1,11)-polarized abelian surfaces is unirational