The classification of automorphisms and quotients of Calabi-Yau threefolds of type A

Pub Date : 2024-08-30 DOI:10.1016/j.jpaa.2024.107796
Martina Monti
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Abstract

The aim of the paper is to investigate the only two families FGA of Calabi-Yau 3-folds A/G with A an abelian 3-fold and GAut(A) a finite group acting freely: one is constructed in [11] and the other is presented here. We provide a complete classification of the automorphism group of XFGA. Additionally, we construct and classify the quotients X/ϒ for any ϒAut(X). Specifically, for those groups ϒ that preserve the volume form of X then X/ϒ admits a desingularization Y which is a Calabi-Yau 3-fold: we compute the Hodge numbers and the fundamental group of these Y, thereby determining all topological in-equivalent Calabi-Yau 3-folds obtained in this way.

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A 型 Calabi-Yau 三折的自形和商的分类
本文旨在研究 Calabi-Yau 3 折叠体中仅有的两个具有无常 3 折叠体和自由作用有限群的系列:一个是在《......》中构建的,另一个是在本文中提出的。我们提供了.的自变群的完整分类。 此外,我们还构造并分类了任意.的商。具体地说,对于那些保留其体积形式的群ϒ,我们会给出一个卡拉比优 3 折叠的去奇化:我们计算了这些群的霍奇数和基群,从而确定了以这种方式得到的所有拓扑内等价卡拉比优 3 折叠。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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