2025/05/19 by Matsubara-Heo, Saiei-Jaeyeong
#Algebraic Geometry (math.AG) #FOS: Mathematics #FOS: Physical sciences #High Energy Physics - Theory (hep-th)
paper · doi:10.48550/arxiv.2505.13163
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.