$F$-purity and the $F$-pure threshold as invariants of linkage
Fuente:
arXiv
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866916340459110400 |
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| author | Pandey, Vaibhav |
| author_facet | Pandey, Vaibhav |
| contents | The generic link of an unmixed radical ideal is radical (in fact, prime). We show that the squarefreeness of the initial ideal and $F$-purity are, however, not preserved along generic links. On the flip side, for several important cases in liaison theory, including generic height three Gorenstein ideals and the maximal minors of a generic matrix, we show that the squarefreeness of the initial ideal, $F$-purity, and the $F$-pure threshold are each preserved along generic links by identifying a property of such ideals which propagates along generic links. We use this property to establish the $F$-regularity of the generic links of such ideals. Finally, we study the $F$-pure threshold of the generic residual intersections of a complete intersection ideal and answer a related question of Kim--Miller--Niu. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2406_05323 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | $F$-purity and the $F$-pure threshold as invariants of linkage Pandey, Vaibhav Commutative Algebra Algebraic Geometry 13C40, 13A35, 14M06 (Primary) 14M10, 14M12 (Secondary) The generic link of an unmixed radical ideal is radical (in fact, prime). We show that the squarefreeness of the initial ideal and $F$-purity are, however, not preserved along generic links. On the flip side, for several important cases in liaison theory, including generic height three Gorenstein ideals and the maximal minors of a generic matrix, we show that the squarefreeness of the initial ideal, $F$-purity, and the $F$-pure threshold are each preserved along generic links by identifying a property of such ideals which propagates along generic links. We use this property to establish the $F$-regularity of the generic links of such ideals. Finally, we study the $F$-pure threshold of the generic residual intersections of a complete intersection ideal and answer a related question of Kim--Miller--Niu. |
| title | $F$-purity and the $F$-pure threshold as invariants of linkage |
| topic | Commutative Algebra Algebraic Geometry 13C40, 13A35, 14M06 (Primary) 14M10, 14M12 (Secondary) |
| url | https://arxiv.org/abs/2406.05323 |