Singularities of square-free polynomials
Algebraic Geometry
2025-05-13 v2 Commutative Algebra
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].
Cite
@article{arxiv.2412.11309,
title = {Singularities of square-free polynomials},
author = {Daniel Bath and Mircea Mustaţă and Uli Walther},
journal= {arXiv preprint arXiv:2412.11309},
year = {2025}
}
Comments
9 pages; v.2: revised version, incorporating the referee's suggestions. Several references have been added