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ON THE DERIVATION LIE ALGEBRAS OF FEWNOMIAL SINGULARITIES

Part of: Local theory Singularities

Published online by Cambridge University Press:  03 May 2018

NAVEED HUSSAIN ,
STEPHEN S.-T. YAU  and
HUAIQING ZUO
NAVEED HUSSAIN
Affiliation:
Department of Mathematical Sciences, Tsinghua University, Beijing 100084, PR China email hnw15@mails.tsinghua.edu.cn
STEPHEN S.-T. YAU*
Affiliation:
Department of Mathematical Sciences, Tsinghua University, Beijing 100084, PR China email yau@uic.edu
HUAIQING ZUO
Affiliation:
Yau Mathematical Sciences Center, Tsinghua University, Beijing 100084, PR China email hqzuo@math.tsinghua.edu.cn
*
✉yau@uic.edu
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Abstract

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Let $V$ be a hypersurface with an isolated singularity at the origin defined by the holomorphic function $f:(\mathbb{C}^{n},0)\rightarrow (\mathbb{C},0)$. The Yau algebra, $L(V)$, is the Lie algebra of derivations of the moduli algebra of $V$. It is a finite-dimensional solvable algebra and its dimension $\unicode[STIX]{x1D706}(V)$ is the Yau number. Fewnomial singularities are those which can be defined by an $n$-nomial in $n$ indeterminates. Yau and Zuo [‘A sharp upper estimate conjecture for the Yau number of weighted homogeneous isolated hypersurface singularity’, Pure Appl. Math. Q.12(1) (2016), 165–181] conjectured a bound for the Yau number and proved that this conjecture holds for binomial isolated hypersurface singularities. In this paper, we verify this conjecture for weighted homogeneous fewnomial surface singularities.

Keywords

fewnomial singularityLie algebraisolated singularity

MSC classification

Primary: 14B05: Singularities
Secondary: 32S05: Local singularities
Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 98 , Issue 1 , August 2018 , pp. 77 - 88
Copyright
© 2018 Australian Mathematical Publishing Association Inc. 

Footnotes

Research partially supported by NSFC (grant nos. 11531007 and 11771231), Tsinghua University Initiative Scientific Research Program and start-up fund from Tsinghua University.

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