Hilbert–Kunz Multiplicities in Families of Certain Two-Dimensional, ℕ-Graded Rings

Abstract

We generalize a theorem of Monsky to compute the Hilbert-Kunz multiplicity of -graded rings k X Y Z / F , where F is a quasi-homogeneous, regular trinomial. This result will be used to study a limit of the Hilbert-Kunz multiplicity in families of such rings, where one exponent of F is dominating the others.