HILBERT-KUNZ MULTIPLICITIES IN FAMILIES OF CERTAIN TWO-DIMENSIONAL, N-GRADED RINGS

摘要

We generalize a theorem of Monsky to compute the Hilbert-Kunz multiplicity of N-graded rings kX, 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.