This research proves that hypersurfaces from irreducible square-free polynomials have rational singularities, suggesting broader implications for related polynomial classes.
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 [2].
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Bath et al. (2025) studied this question.
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