English

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].

Keywords

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

R2 v1 2026-06-28T20:36:00.958Z