Singularities of square-free polynomials

TL;DR

This paper proves that hypersurfaces defined by irreducible square-free polynomials have rational singularities, extending known results to broader classes of polynomials related to matroids and Feynman diagrams.

Contribution

It establishes the rational singularities of hypersurfaces from irreducible square-free polynomials and related polynomials, broadening the scope of previous results.

Findings

Hypersurfaces from irreducible square-free polynomials have rational singularities.

Certain polynomials related to matroids and Feynman diagrams also define hypersurfaces with rational singularities.

Abstract

We prove that hypersurfaces defined by irreducible square-free polynomials have rational singularities. As an easy consequence, we deduce that certain (possibly non-square-free) polynomials associated to pairs of square-free polynomials define hypersurfaces with rational singularities. This extends results on certain classes of polynomials associated to matroids and Feynman diagrams in [BW].