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arXiv · 1404.3772

F-pure thresholds of homogeneous polynomials

Daniel J. Hernández·Luis Núñez-Betancourt·Emily E. Witt·Wenliang Zhang
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Abstract

In this article, we investigate F-pure thresholds of polynomials that are homogeneous under some N-grading, and have an isolated singularity at the origin. We characterize these invariants in terms of the base p expansion of the corresponding log canonical threshold. As an application, we are able to make precise some bounds on the difference between F-pure and log canonical thresholds established by Mustaţă and the fourth author. We also examine the set of primes for which the F-pure and log canonical threshold of a polynomial must differ. Moreover, we obtain results in special cases on the ACC conjecture for F-pure thresholds, and on the upper semi-continuity property for the F-pure threshold function.

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Daniel J. Hernández, Luis Núñez-Betancourt, Emily E. Witt, Wenliang Zhang. 2014-04-14. F-pure thresholds of homogeneous polynomials. https://arxiv.org/abs/1404.3772

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