Communications in Analysis and Geometry

Volume 30 (2022)

Number 8

Complex structures of a twenty-dimensional family of Calabi–Yau $3$-folds

Pages: 1825 – 1831

DOI: https://dx.doi.org/10.4310/CAG.2022.v30.n8.a6

Authors

Chuangqiang Hu (Yau Mathematical Sciences Center, Tsinghua University, Beijing, China)

Stephen S.-T. Yau (Department of Mathematical Sciences, Tsinghua University, Beijing, China)

Huaiqing Zuo (Department of Mathematical Sciences, Tsinghua University, Beijing, China)

Abstract

In this paper, we classify all isomorphic classes of a family of Calabi–Yau $3$-folds with $20$ parameters. In addition, we show that the isomorphisms form a finite group. The invariants under the action of this group are calculated by introducing the so-called DS‑graph.

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Both Yau and Zuo are supported by NSFC Grants 11961141005. Zuo is supported by NSFC Grant 12271280. Hu is supported by NSFC Grants 12071247 and 12101616. Yau is supported by Tsinghua university start-up fund and Tsinghua university education foundation fund (042202008).

Received 24 October 2019

Accepted 5 March 2020

Published 13 July 2023