$F$-pure thresholds and $F$-Volumes of some non principal ideals
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arXiv
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| Format: | Preprint |
| Published: |
2023
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| _version_ | 1866912433952522240 |
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| author | Badilla-Céspedes, Wágner León-Cardenal, Edwin |
| author_facet | Badilla-Céspedes, Wágner León-Cardenal, Edwin |
| contents | We compute the $F$-pure threshold of some non-principal ideals which satisfy a geometric generic condition about their Newton polyhedron. We also contribute some evidence in favor of the conjectured equality between the $F$-pure threshold and the log canonical threshold of ideals for infinitely many primes $p$. These results are obtained by generalizing the theory of splitting polytopes to the case of ideals. As an application of our results we obtain geometric lower bounds for the recently introduced $F$-volume of a collection of ideals. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2305_00571 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | $F$-pure thresholds and $F$-Volumes of some non principal ideals Badilla-Céspedes, Wágner León-Cardenal, Edwin Commutative Algebra Algebraic Geometry 13A35, 14B05, 14M25 We compute the $F$-pure threshold of some non-principal ideals which satisfy a geometric generic condition about their Newton polyhedron. We also contribute some evidence in favor of the conjectured equality between the $F$-pure threshold and the log canonical threshold of ideals for infinitely many primes $p$. These results are obtained by generalizing the theory of splitting polytopes to the case of ideals. As an application of our results we obtain geometric lower bounds for the recently introduced $F$-volume of a collection of ideals. |
| title | $F$-pure thresholds and $F$-Volumes of some non principal ideals |
| topic | Commutative Algebra Algebraic Geometry 13A35, 14B05, 14M25 |
| url | https://arxiv.org/abs/2305.00571 |