Asian Journal of Mathematics

Volume 26 (2022)

Number 3

Non-existence of negative weight derivations of the local $1\textrm{-st}$ Hessian algebras of singularities

Pages: 289 – 372

DOI: https://dx.doi.org/10.4310/AJM.2022.v26.n3.a1

Authors

Shuanghe Fan (Department of Mathematical Sciences, Tsinghua University, Beijing, China)

Stephen S.-T. Yau (Department of Mathematical Sciences, Tsinghua University, Beijing, China; and Yanqi Lake Beijing Institute of Mathematical Sciences and Applications, Beijing, China)

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

Abstract

In our previous work, we proposed a conjecture about the non-existence of negative weight derivations of the $k\textrm{-st}$ Tjurina algebras of weighted homogeneous hypersurface singularities. In this paper, we verify this conjecture for three dimensional fewnomial singularities.

Keywords

derivation Lie algebra, isolated singularity, weighted homogeneous

2010 Mathematics Subject Classification

14B05, 32S05

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Both Yau and Zuo are supported by NSFC Grant 11961141005. Zuo is also supported by NSFC Grant 12271280, and by the Tsinghua University Initiative Scientific Research Program. Yau is also supported by Tsinghua University start-up fund, and by the Tsinghua University Education Foundation fund (042202008).

Received 8 October 2021

Accepted 7 February 2022

Published 6 March 2023