Explicit reconstruction of homogeneous isolated hypersurface singularities from their Milnor algebras
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Abstract:
By the Mather-Yau theorem, a complex hypersurface germ ${\mathcal V}$ with isolated singularity is completely determined by its moduli algebra ${\mathcal A}({\mathcal V})$. The proof of the theorem does not provide an explicit procedure for recovering ${\mathcal V}$ from ${\mathcal A}({\mathcal V})$, and finding such a procedure is a long-standing open problem. In this paper, we present an explicit way for reconstructing ${\mathcal V}$ from ${\mathcal A}({\mathcal V})$ up to biholomorphic equivalence under the assumption that the singularity of ${\mathcal V}$ is homogeneous, in which case ${\mathcal A}({\mathcal V})$ coincides with the Milnor algebra of ${\mathcal V}$.References
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Additional Information
- A. V. Isaev
- Affiliation: Department of Mathematics, The Australian National University, Canberra, ACT 0200, Australia
- MR Author ID: 241631
- Email: alexander.isaev@anu.edu.au
- N. G. Kruzhilin
- Affiliation: Department of Complex Analysis, Steklov Mathematical Institute, 8 Gubkina Street, Moscow GSP-1 119991, Russia
- Email: kruzhil@mi.ras.ru
- Received by editor(s): March 25, 2012
- Published electronically: October 31, 2013
- Communicated by: Franc Forstneric
- © Copyright 2013
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Proc. Amer. Math. Soc. 142 (2014), 581-590
- MSC (2010): Primary 32S25, 13H10
- DOI: https://doi.org/10.1090/S0002-9939-2013-11822-8
- MathSciNet review: 3133999