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Nonexistence of negative weight derivations of the local $k$-th Hessian algebras associated to isolated singularities

Guorui Ma, Stephen S.-T. Yau and Huaiqing Zuo

Vol. 323 (2023), No. 1, 129–172
DOI: 10.2140/pjm.2023.323.129
Abstract

A new conjecture about the nonexistence of negative weight derivations of the k-th Hessian algebras for weighted homogeneous isolated hypersurface singularities is proposed. We verify this conjecture up to dimension three.

Keywords
derivations, Hessian algebra, isolated singularity, weighted homogeneous
Mathematical Subject Classification
Primary: 14B05, 32S05
Milestones
Received: 9 June 2022
Revised: 13 September 2022
Accepted: 9 October 2022
Published: 29 May 2023
Authors
Guorui Ma
Yau Mathematical Sciences Center
Tsinghua University
Beijing
China
Stephen S.-T. Yau
Department of Mathematical Sciences
Tsinghua University
Beijing
China
Yanqi Lake Beijing Institute of Mathematical Sciences and Applications
Huairou
China
Huaiqing Zuo
Department of Mathematical Sciences
Tsinghua University
Beijing
China

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