Extracting invariants of isolated hypersurface singularities from their moduli algebras

被引：0
作者：
M. G. Eastwood
A. V. Isaev
机构：
[1] The Australian National University,Mathematical Sciences Institute
来源：
Mathematische Annalen | 2013年 / 356卷
关键词：
32S25; 13H10; 13A50;
D O I：
暂无
中图分类号：
学科分类号：
摘要：
We use classical invariant theory to construct invariants of complex graded Gorenstein algebras of finite vector space dimension. As a consequence, we obtain a way of extracting certain numerical invariants of quasi-homogeneous isolated hypersurface singularities from their moduli algebras, which extends an earlier result due to the first author. Furthermore, we conjecture that the invariants so constructed solve the biholomorphic equivalence problem in the homogeneous case. The conjecture is easily verified for binary quartics and ternary cubics. We show that it also holds for binary quintics and sextics. In the latter cases the proofs are much more involved. In particular, we provide a complete list of canonical forms of binary sextics, which is a result of independent interest.
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页码：73 / 98
页数：25
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