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.
ON THE EXISTENCE OF F-THRESHOLDS AND RELATED LIMITS
De Stefani A;
2018-01-01
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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