arXiv subjects

Raul Epure

Publications and source records attributed to Raul Epure.

3 recordsLinked to original sources

arXiv2022

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.

math.AG↗

arXiv2020

On Constructions of Free Singularities

The purpose of this paper is to give new examples of families of free singularities. We first show that a generic equidimensional subspace arrangement is free. Furthermore, we show that a product of two reduced Cohen-Macaulay subspaces is free if and only if both subspaces are free.

math.AG↗

arXiv2018

A Saito criterion for holonomic divisors

We show that a holonomic divisor is free if and only if applying all logarithmic derivations to a generic function with isolated critical point yields a complete intersection Artin algebra.

math.AG↗