Surveys in Differential Geometry

Volume 23 (2018)

Recent results on $k$-th Yau algebras over simple elliptic singularities $\tilde{E}_6$

Pages: 213 – 240

DOI: https://dx.doi.org/10.4310/SDG.2018.v23.n1.a5

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

Recently, we have introduced a series of finite dimensional solvable Lie algebras (i.e., $k$‑th Yau algebras) associated to an isolated hypersurface singularity. These Lie algebras are subtle invariants of singularities. The purpose of this paper is to summarize the results that we have obtained recently on $k$‑th moduli algebras and $k$‑th Yau algebras associated to isolated hypersurface singularities.

Keywords

Torelli theorem, elliptic singularity, derivation Lie algebra, $k$-th Yau algebra

2010 Mathematics Subject Classification

14B05, 32S05

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Both Yau and Zuo are supported by NSFC Grants 11961141005 and 11531007. Zuo is supported by NSFC Grant 11771231. Yau is supported by Tsinghua university start-up fund and Tsinghua university education foundation fund (042202008).

Published 5 May 2020