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arXiv · 2610.29204

The Logarithmic A-Discriminant

Madeleine Goertz·Bernd Sturmfels·Simon Telen
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Abstract

We extend the GKZ theory of discriminants to the setting of Euler integrals where both coefficients and exponents are variables. The integrand is the likelihood function of a toric model in algebraic statistics, whose number of critical points is the volume of the Newton polytope. Our logarithmic A-discriminant vanishes when two critical points come together. This discriminant is a hypersurface, parametrized by the logarithmic Horn uniformization. Hurwitz forms of toric varieties yield a degree formula, and a description of leading coefficients. We emphasize applications and computations.

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Madeleine Goertz, Bernd Sturmfels, Simon Telen. 2026-10-21. The Logarithmic A-Discriminant. https://arxiv.org/abs/2610.29204

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