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arXiv · 2005.09172

$F$-thresholds and test ideals of Thom-Sebastiani type polynomials

Manuel González Villa·Delio Jaramillo-Velez·Luis Núñez-Betancourt
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Abstract

We provide a formula for $F$-thresholds of a Thom-Sebastiani type polynomial over a perfect field of prime characteristic. This result extends the formula for the $F$-pure threshold of a diagonal hypersurface. We also compute the first test ideal of Thom-Sebastiani type polynomials. Finally, we apply our result to find hypersurfaces where the log canonical thresholds equals the $F$-pure thresholds for infinitely many prime numbers.

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Manuel González Villa, Delio Jaramillo-Velez, Luis Núñez-Betancourt. 2020-05-19. $F$-thresholds and test ideals of Thom-Sebastiani type polynomials. https://arxiv.org/abs/2005.09172

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