Hypersurface singularities with monomial Jacobian ideal
- We show that every convergent power series with monomial extended Jacobian ideal is right equivalent to a Thom–Sebastiani polynomial. This solves a problem posed by Hauser and Schicho. On the combinatorial side, we introduce a notion of Jacobian semigroup ideal involving a transversal matroid. For any such ideal, we construct a defining Thom–Sebastiani polynomial. On the analytic side, we show that power series with a quasihomogeneous extended Jacobian ideal are strongly Euler homogeneous. Due to a Mather–Yau-type theorem, such power series are determined by their Jacobian ideal up to right equivalence.
Author: | Raul Epure, Mathias Schulze |
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URN: | urn:nbn:de:hbz:386-kluedo-80288 |
DOI: | https://doi.org/10.1112/blms.12614 |
ISSN: | 1469-2120 |
Parent Title (English): | Bulletin of the London Mathematical Society |
Publisher: | Wiley |
Document Type: | Article |
Language of publication: | English |
Date of Publication (online): | 2024/04/15 |
Year of first Publication: | 2021 |
Publishing Institution: | Rheinland-Pfälzische Technische Universität Kaiserslautern-Landau |
Date of the Publication (Server): | 2024/04/15 |
Issue: | 54/3 |
Page Number: | 15 |
First Page: | 1067 |
Last Page: | 1081 |
Source: | https://londmathsoc.onlinelibrary.wiley.com/doi/10.1112/blms.12614 |
Faculties / Organisational entities: | Kaiserslautern - Fachbereich Mathematik |
DDC-Cassification: | 5 Naturwissenschaften und Mathematik / 510 Mathematik |
Collections: | Open-Access-Publikationsfonds |
Licence (German): | Zweitveröffentlichung |