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arXiv · 2101.04069

Hypersurface singularities with monomial Jacobian ideal

Raul Epure·Mathias Schulze
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Abstract

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.

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Raul Epure, Mathias Schulze. 2021-01-11. Hypersurface singularities with monomial Jacobian ideal. https://doi.org/10.1112/blms.12614

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