Inversion of adjunction for F-signature

2019/09/23 by Gregory Taylor, Taylor, Gregory · 1 citation
Mathematics · #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Commutative Algebra (math.AC) #Commutative Algebra and Its Applications #FOS: Mathematics #Geometry and complex manifolds

paper · pdf · doi:10.48550/arxiv.1909.10436

openalex publication_date 2019/09/23 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let (R,Δ+D) be a log ℚ-Gorenstein pair where R is a Noetherian, F-finite, normal, local domain of characteristic p > 0, Δ is an effective ℚ-divisor and D is an integral ℚ-Cartier divisor. We show that the left derivative of the F-signature function s(R,Δ+ tD) at t = 1 is equal to -s(O_D, Diff_D(Δ)). This equality is interpreted as a quantitative form of inversion of adjunction for strong F-regularity. As an immediate corollary, we obtain the inequality s(R,Δ) ≥ s(O_D, Diff_D(Δ)). We also discuss the implications of our result for the conjectured connection between the F-signature and the normalized volume.

Citations

• F-Signature of Affine Toric Varieties

Cited by

• On the uniform positivity of F-signature under reduction modulo p

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