Plus-pure thresholds of some cusp-like singularities in mixed characteristic

2025/01/13 by Cai, Hanlin, Pande, Suchitra, Quinlan-Gallego, Eamon +2 · 1 citation
#Algebraic Geometry (math.AG) #Commutative Algebra (math.AC) #FOS: Mathematics

paper · doi:10.48550/arxiv.2501.07528

Abstract

Log-canonical and F-pure thresholds of pairs in equal characteristic admit an analog in the recent theory of singularities in mixed characteristic, which is known as the plus-pure threshold. In this paper we study plus-pure thresholds for singularities of the form p^a + x^b ∈ \bf Z_p [[ x ]], showing that in a number of cases this plus-pure threshold agrees with the F-pure threshold of the singularity t^a + x^b ∈ \bf F_p [[ t, x ]]. We also discuss a few other sporadic examples.

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