Calabi-Yau Three-folds and Moduli of Abelian Surfaces II

TL;DR

This paper completes the classification of moduli spaces of low-degree polarized abelian surfaces, providing birational models and discovering new Calabi-Yau threefolds fibred in abelian surfaces.

Contribution

It offers a detailed description of moduli spaces for specific low degrees and introduces new Calabi-Yau threefolds fibred in abelian surfaces.

Findings

Moduli spaces are rational or unirational.

Birational models for each degree case are constructed.

New Calabi-Yau threefolds fibred in abelian surfaces are described.

Abstract

This is the sequel to arXiv:math/0001089. In this paper, we complete the promised description of moduli of abelian surfaces of low degree, covering the cases of degree (1,12), (1,14), (1,16), (1,18) and (1,20). In each case, we describe birational models for the moduli space of abelian surfaces with polarization of the given degree and either a level structure, or what we call a partial level structure. In every case, the moduli space is rational or unirational. In additional, several new Calabi-Yau threefolds fibred in abelian surfaces are described.