English

The F-signature of an affine semigroup ring

Commutative Algebra 2007-05-23 v1

Abstract

We prove that the F-signature of an affine semigroup ring of positive characteristic is always a rational number, and describe a method for computing this number. We use this method to determine the F-signature of Segre products of polynomial rings, and of Veronese subrings of polynomial rings. Our technique involves expressing the F-signature of an affine semigroup ring as the difference of the Hilbert-Kunz multiplicities of two monomial ideals, and then using Watanabe's result that these Hilbert-Kunz multiplicities are rational numbers.

Keywords

Cite

@article{arxiv.math/0409143,
  title  = {The F-signature of an affine semigroup ring},
  author = {Anurag K. Singh},
  journal= {arXiv preprint arXiv:math/0409143},
  year   = {2007}
}