Relating F-Signature and F-Splitting Ratio of Pairs Using Left-Derivatives

2012/06/19 by Eric Canton, Canton, Eric
Computer Science · Mathematics · #Advanced Algebra and Geometry #Algebraic Geometry and Number Theory #Commutative Algebra (math.AC) #FOS: Mathematics #Polynomial and algebraic computation

paper · pdf · doi:10.48550/arxiv.1206.4293

openalex publication_date 2012/06/19 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28

Abstract

We first relate an approximate n^th-order left derivative of s(R, f^t) at the F-pure threshold c to the F-splitting ratio r_F(R, f^c). Next, we apply the methods developed by Monsky and Teixeira in their investigation of syzygy gaps and p-fractals to obtain uniform convergence of the F-signature when f is a product of distinct linear polynomials in two variables. Finally, we explicitly compute the F-signature function for several examples using Macaulay2 code outlined in the last section of this paper.

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