On the derivation Lie algebras of fewnomial singularities

Hussain, Naveed Tsinghua University Stephen.S.-T. Yau Tsinghua University Huaiqing Zuo Tsinghua University


Bull. Aust. Math. Soc., 98, (1), 77-88, 2018.2
Let V be a hypersurface with an isolated singularity at the origin de- fined by the holomorphic function f : (Cn, 0) → (C, 0). L(V ) is defined to be the Lie algebra of derivations of the moduli algebra A(V ) := On/(f, ∂f , · · · , ∂f ), i.e. ∂x1 ∂xn L(V ) = Der(A(V ), A(V )). The Lie algebra L(V ) is finite dimensional solvable alge- bra and plays an important role in singularity theory. L(V ) is called Yau algebra and λ(V ), the dimension of L(V ), is called Yau number. Fewnomial singularities are those which can be defined by n-nomial in n indeterminates. These singularities were inten- sively studied from a mirror symmetry point of view by many other mathematicians. Here we investigate these singularities from a Yau algebra point of view. In our previous work, we formulated a sharp upper estimate conjecture for the Yau numbers of weighted homogeneous isolated hypersurface singularities and proved that this conjecture holds for binomial isolated hypersurface singularities. In this paper we verify this conjecture for weighted homogeneous fewnomial surface singularities.
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  title={ On the derivation Lie algebras of fewnomial singularities},
  author={Hussain, Naveed, Stephen.S.-T. Yau, and Huaiqing Zuo},
  booktitle={ Bull. Aust. Math. Soc.},
Hussain, Naveed, Stephen.S.-T. Yau, and Huaiqing Zuo. On the derivation Lie algebras of fewnomial singularities. 2018. Vol. 98. In Bull. Aust. Math. Soc.. pp.77-88. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20190311161143413576197.
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