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The F-signature of an affine semigroup ring

Anurag K. Singh
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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.

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Anurag K. Singh. 2004-09-09. The F-signature of an affine semigroup ring. https://arxiv.org/abs/math/0409143

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