The Logarithmic A-Discriminant
Madeleine Goertz, Bernd Sturmfels, Simon Telen
Source 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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