Some Siegel threefolds with a Calabi-Yau model II

TL;DR

This paper expands the list of Siegel modular threefolds that admit a Calabi-Yau model by employing a new method based on desingularization and holomorphic three-forms, building on prior work.

Contribution

It introduces a novel approach to identify Siegel threefolds with Calabi-Yau models, broadening the known examples using desingularization techniques.

Findings

Expanded list of Siegel threefolds with Calabi-Yau models

New method based on desingularization and holomorphic forms

Identification of varieties with vanishing first Betti number

Abstract

In the paper [FSM] we described some Siegel modular threefolds which admit a Calabi-Yau model. Using a different method we give in this paper an enlarged list of such varieties that admits a Calabi-Yau model in the following weak sense: there exists a desingularization in the category of complex spaces of the Satake compactification which admits a holomorphic three-form without zeros and whose first Betti number vanishes Basic for our method is the paper [GN] of van Geemen and Nygaard.