The hilbert-kunz function in graded dimension two

摘要

Let R denote a two-dimensional normal standard-graded K-domain over the algebraic closure K of a finite field of characteristic p, and let I subset of R denote a homogeneous R+-primary ideal. We prove that the Hilbert-Kunz function of I has the form phi(q)= e(HK)(I)q(2) + gamma(q) with rational Hilbert-Kunz multiplicity e(HK)(I) and an eventually periodic function gamma(q).