Comptes Rendus
Analyse et géométrie complexes
On the Thom–Sebastiani Property of Quasi-Homogeneous Isolated Hypersurface Singularities
Raul Epure1
1 Gottlieb-Daimler-Straße 48, 67663 Kaiserslautern, Germany
Comptes Rendus. Mathématique, Volume 360 (2022), pp. 539-547.

Let (V,0)⊂(ℂ n ,0) be a quasi-homogeneous isolated hypersurface singularity. In this paper we prove under certain weight conditions a relation between the property of (V,0) being of Thom–Sebastiani type and the dimension of toral Lie subalgebras contained in the Yau algebra L(V).

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DOI : 10.5802/crmath.324
Classification : 32S25
Raul Epure 1

1 Gottlieb-Daimler-Straße 48, 67663 Kaiserslautern, Germany
Licence : CC-BY 4.0
Droits d'auteur : Les auteurs conservent leurs droits 
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     title = {On the {Thom{\textendash}Sebastiani} {Property} of {Quasi-Homogeneous} {Isolated} {Hypersurface} {Singularities}},
     journal = {Comptes Rendus. Math\'ematique},
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     year = {2022},
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     language = {en},
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Raul Epure. On the Thom–Sebastiani Property of Quasi-Homogeneous Isolated Hypersurface Singularities. Comptes Rendus. Mathématique, Volume 360 (2022), pp. 539-547. doi : 10.5802/crmath.324. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.324/

[1] Bingyi Chen; Naveed Hussain; Stephen S.-T. Yau; Huaiqing Zuo Variation of complex structures and variation of Lie algebras II: new Lie algebras arising from singularities, J. Differ. Geom., Volume 115 (2020) no. 3, pp. 437-473 | DOI | MR | Zbl

[2] Wolfram Decker; Gert-Martin Greuel; Gerhard Pfister; Hans Schönemann Singular 4-2-1 — A computer algebra system for polynomial computations, http://www.singular.uni-kl.de, 2021

[3] Raul-Paul Epure Explicit and effective Mather–Yau correspondence in view of analytic gradings, doctoralthesis, Technische Universität Kaiserslautern (2020), II, 170, V pages http://nbn-resolving.de/urn:nbn:de:hbz:386-kluedo-61500

[4] Raul-Paul Epure; Mathias Schulze Hypersurface singularities with monomial Jacobian ideal, Bull. Lond. Math. Soc. (2022) (https://doi.org/10.1112/blms.12614) | DOI

[5] Herwig Hauser; Gerd Müller On the Lie algebra Θ (X) of vector fields on a singularity, J. Math. Sci., Tokyo, Volume 1 (1994), pp. 239-250 | MR | Zbl

[6] James E. Humphreys Linear algebraic groups, Graduate Texts in Mathematics, 21, Springer, 1975, xiv+247 pages | MR

[7] Naveed Hussain; Stephen S.-T. Yau; Huaiqing Zuo On the new k-th Yau algebras of isolated hypersurface singularities, Math. Z., Volume 294 (2020), pp. 1-28 | DOI | MR | Zbl

[8] Naveed Hussain; Stephen S.-T. Yau; Huaiqing Zuo k-th Yau number of isolated hypersurface singularities and An Inequality Conjecture, J. Aust. Math. Soc., Volume 110 (2021), 1650, 15 pages | DOI | MR

[9] Naveed Hussain; Stephen S.-T. Yau; Huaiqing Zuo On the Dimension of a New Class of Derivation Lie Algebras Associated to Singularities, Mathematics, Volume 9 (2021) no. 14 | DOI

[10] Theo de Jong; Gerhard Pfister Local analytic geometry. Basic theory and applications, Advanced Lectures in Mathematics (ALM), Vieweg & Sohn, 2000, xii+382 pages | DOI | MR | Zbl

[11] Martin Kreuzer; Lorenzo Robbiano Computational Commutative Algebra. II, Springer, 2005 | Zbl

[12] John N. Mather; Stephen S.-T. Yau Classification of isolated hypersurface singularities by their moduli algebras, Invent. Math., Volume 69 (1982) no. 2, pp. 243-251 | DOI | MR | Zbl

[13] Dan Roozemond Algorithms for Lie algebras of algebraic groups, Ph. D. Thesis, Technische Universiteit Eindhoven (2010)

[14] Kyoji Saito Quasihomogene isolierte Singularitäten von Hyperflächen, Invent. Math., Volume 14 (1971), pp. 123-142 | DOI | MR | Zbl

[15] Günter Scheja; Hartmut Wiebe Über Derivationen von lokalen analytischen Algebren, Symposia Mathematica, Vol. XI (Convegno di Algebra Commutativa, INDAM, Rome, 1971), Academic Press Inc., 1973, pp. 161-192 | MR | Zbl

[16] Yi-Jing Xu; Stephen S.-T. Yau Micro-local characterization of quasi-homogeneous singularities, Am. J. Math., Volume 118 (1996) no. 2, pp. 389-399 | MR | Zbl

[17] Stephen S.-T. Yau A necessary and sufficient condition for a local commutative algebra to be a moduli algebra: weighted homogeneous case, Complex analytic singularities (Advanced Studies in Pure Mathematics), Volume 8, North-Holland, 1987, pp. 687-697 | DOI | MR | Zbl

[18] Stephen S.-T. Yau; Huaiqing Zuo Derivations of the moduli algebras of weighted homogeneous hypersurface singularities, J. Algebra, Volume 457 (2016), pp. 18-25 | DOI | MR | Zbl

[19] Stephen S.-T. Yau; Huaiqing Zuo Sharp upper estimate conjecture for the Yau number of a weighted homogeneous isolated hypersurface singularity, Pure Appl. Math. Q., Volume 12 (2016), pp. 165-181 | DOI | MR | Zbl

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