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arXiv · 1605.03264

On the existence of $F$-thresholds and related limits

Alessandro De Stefani·Luis Núñez-Betancourt·Felipe Pérez
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Abstract

The $F$-thresholds are important numerical invariants in prime characteristic, whose existence had been established only under certain assumptions. We show the existence of $F$-thresholds in full generality. 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 existence of related limits in certain cases.

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Alessandro De Stefani, Luis Núñez-Betancourt, Felipe Pérez. 2017-01-11. On the existence of $F$-thresholds and related limits. https://arxiv.org/abs/1605.03264

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