The $F$-pure threshold of a Schubert cycle
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866915458677997568 |
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| author | Fong, Justin Miyazaki, Mitsuhiro |
| author_facet | Fong, Justin Miyazaki, Mitsuhiro |
| contents | The $F$-pure threshold is the characteristic $p$ counter part of the log canonical threshold in characteristic zero. It is a numerical invariant associated to the singularities of a variety, hence computing its value is important. We give a closed formula for the $F$-pure threshold of the irrelevant maximal ideal of Schubert cycles, which are the homogeneous coordinate rings of Schubert subvarieties of a Grassmannian. The main point of the computation is to give an explicit formula for the $a$-invariant of a Schubert cycle. The derivation of both formulas is made possible through the combinatorics of the underlying poset of these rings. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2502_09559 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | The $F$-pure threshold of a Schubert cycle Fong, Justin Miyazaki, Mitsuhiro Commutative Algebra The $F$-pure threshold is the characteristic $p$ counter part of the log canonical threshold in characteristic zero. It is a numerical invariant associated to the singularities of a variety, hence computing its value is important. We give a closed formula for the $F$-pure threshold of the irrelevant maximal ideal of Schubert cycles, which are the homogeneous coordinate rings of Schubert subvarieties of a Grassmannian. The main point of the computation is to give an explicit formula for the $a$-invariant of a Schubert cycle. The derivation of both formulas is made possible through the combinatorics of the underlying poset of these rings. |
| title | The $F$-pure threshold of a Schubert cycle |
| topic | Commutative Algebra |
| url | https://arxiv.org/abs/2502.09559 |