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Isolated Hypersurface Singularities and Special Polynomial Realizations of Affine Quadrics

Fels, G.; Isaev, Alexander; Kaup, W.; Kruzhilin, N.

Description

Let V, Ṽ be hypersurface germs in ℂᵐ , each having a quasi-homogeneous isolated singularity at the origin. We show that the biholomorphic equivalence problem for V, V~V~ reduces to the linear equivalence problem for certain polynomials P, P~ arising from the moduli algebras of V, Ṽ. The polynomials P, P~ are completely determined by their quadratic and cubic terms, hence the biholomorphic equivalence problem for V, Ṽ in fact reduces to the linear equivalence problem for pairs of quadratic and...[Show more]

dc.contributor.authorFels, G.
dc.contributor.authorIsaev, Alexander
dc.contributor.authorKaup, W.
dc.contributor.authorKruzhilin, N.
dc.date.accessioned2016-03-08T05:35:44Z
dc.date.available2016-03-08T05:35:44Z
dc.identifier.issn1050-6926
dc.identifier.urihttp://hdl.handle.net/1885/100193
dc.description.abstractLet V, Ṽ be hypersurface germs in ℂᵐ , each having a quasi-homogeneous isolated singularity at the origin. We show that the biholomorphic equivalence problem for V, V~V~ reduces to the linear equivalence problem for certain polynomials P, P~ arising from the moduli algebras of V, Ṽ. The polynomials P, P~ are completely determined by their quadratic and cubic terms, hence the biholomorphic equivalence problem for V, Ṽ in fact reduces to the linear equivalence problem for pairs of quadratic and cubic forms.
dc.description.sponsorshipThe research is supported by the Australian Research Council. The fourth author is supported by the Russian Foundation for Basic Research and grant no. NSh-3476.2010.1 of the Leading Scientific Schools program.
dc.publisherAmerican Mathematical Society
dc.rights© Mathematica Josephina, Inc. 2011
dc.sourceJournal of Geometric Analysis
dc.subjectIsolated hypersurface singularities
dc.subjectGorenstein algebras
dc.titleIsolated Hypersurface Singularities and Special Polynomial Realizations of Affine Quadrics
dc.typeJournal article
local.description.notesImported from ARIES
local.identifier.citationvolume21
dc.date.issued2011
local.identifier.absfor010111
local.identifier.absfor010101
local.identifier.ariespublicationf2965xPUB2020
local.publisher.urlhttp://link.springer.com/
local.type.statusPublished Version
local.contributor.affiliationFels, G, Universität Tübingen, Germany
local.contributor.affiliationIsaev, Alexander, College of Physical and Mathematical Sciences, CPMS Mathematical Sciences Institute, Department of Mathematics, The Australian National University
local.contributor.affiliationKaup, W, Universität Tübingen, Germany
local.contributor.affiliationKruzhilin, Nikolay, College of Physical and Mathematical Sciences, CPMS Mathematical Sciences Institute, Centre for Mathematics and Its Applications, The Australian National University
local.bibliographicCitation.issue3
local.bibliographicCitation.startpage767
local.bibliographicCitation.lastpage782
local.identifier.doi10.1007/s12220-011-9223-y
local.identifier.absseo970101
dc.date.updated2016-06-14T08:35:03Z
local.identifier.scopusID2-s2.0-80051802290
local.identifier.thomsonID000291745600012
CollectionsANU Research Publications

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