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arXiv · 2505.13163

Hypergeometric Discriminants

Saiei-Jaeyeong Matsubara-Heo
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Abstract

Given a family of varieties, the Euler discriminant locus distinguishes points where Euler characteristic differs from its generic value. We introduce a hypergeometric system associated with a flat family of very affine locally complete intersection varieties. It is proven that the Euler discriminant locus is its singular locus and is purely one-codimensional unless it is empty. Of particular interest is a family of very affine hypersurfaces. We coin the term hypergeometric discriminant for the characteristic cycle of the hypergeometric system and establish a formula in terms of likelihood equations.

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Saiei-Jaeyeong Matsubara-Heo. 2025-05-19. Hypergeometric Discriminants. https://arxiv.org/abs/2505.13163

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