Hilbert-Kunz multiplicity of quadrics via Ehrhart theory
Igor Pak, Boris Shapiro, Ilya Smirnov, Ken-ichi Yoshida
Published: 2025/8/25
Abstract
We show that the Hilbert-Kunz multiplicity of the d-dimensional non-degenerate quadric hypersurface of characteristic p > 2 is a rational function of p composed from the Ehrhart polynomials of integer polytopes. In consequence, we explain and recover a result of Gessel and Monsky and prove that the Hilbert-Kunz multiplicity of quadrics of fixed characteristic is a decreasing function of dimension.