F-thresholds of graded rings

2015/07/20 by Alessandro De Stefani, De Stefani, Alessandro, Luis Núñez‐Betancourt +1 · 2 citations
Mathematics · #14B05 #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Algebraic structures and combinatorial models #Commutative Algebra (math.AC) #Commutative Algebra and Its Applications #FOS: Mathematics #Primary 13A35 #Secondary 13H10

paper · pdf · doi:10.48550/arxiv.1507.05459

openalex publication_date 2015/07/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The a-invariant, the F-pure threshold, and the diagonal F-threshold are three important invariants of a graded K-algebra. Hirose, Watanabe, and Yoshida have conjectured relations among these invariants for strongly F-regular rings. In this article, we prove that these relations hold only assuming that the algebra is F-pure. In addition, we present an interpretation of the a-invariant for F-pure Gorenstein graded K-algebras in terms of regular sequences that preserve F-purity. This result is in the spirit of Bertini theorems for projective varieties. Moreover, we show connections with projective dimension, Castelnuovo-Mumford regularity, and Serre's condition S_k. We also present analogous results and questions in characteristic zero.

Cited by

• On the uniform positivity of F-signature under reduction modulo p
• On lower bounds for the F-pure threshold of equigenerated ideals

Related

• The F-pure threshold versus the a-invariant for standard graded rings
• On the existence of F-thresholds and related limits
• The defect of the F-pure threshold
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