On the existence of 𝐹-thresholds and related limits

De Stefani, Alessandro; Núñez-Betancourt, Luis; Pérez, Felipe

doi:10.1090/tran/7176

On the existence of $F$-thresholds and related limits
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by Alessandro De Stefani, Luis Núñez-Betancourt and Felipe Pérez PDF

Trans. Amer. Math. Soc. 370 (2018), 6629-6650 Request permission

Abstract:

We show the existence of $F$-thresholds in full generality. In addition, we study properties of standard graded algebras over a field for which $F$-pure threshold and $F$-threshold at the irrelevant maximal ideal agree. We also exhibit explicit bounds for the $a$-invariants and Castelnuovo-Mumford regularity of Frobenius powers of ideals in terms of $F$-thresholds and $F$-pure thresholds, obtaining the existence of related limits in certain cases.

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