On vanishing of higher direct images of the structure sheaf
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866915250838700032 |
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| author | Ishii, Shihoko Yoshida, Ken-ichi |
| author_facet | Ishii, Shihoko Yoshida, Ken-ichi |
| contents | We show the vanishing of the first direct image of the structure sheaf of a normal scheme $X$ which is mapped properly and birationally over a regular scheme of any dimension. On the other hand, for any dimension greater than two, we show examples of a proper birational morphism from a normal and Cohen-Macaulay scheme to a regular scheme such that the second direct image does not vanish and has an isolated support. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_15282 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On vanishing of higher direct images of the structure sheaf Ishii, Shihoko Yoshida, Ken-ichi Algebraic Geometry Commutative Algebra 13H05, 13A30, 14B05 We show the vanishing of the first direct image of the structure sheaf of a normal scheme $X$ which is mapped properly and birationally over a regular scheme of any dimension. On the other hand, for any dimension greater than two, we show examples of a proper birational morphism from a normal and Cohen-Macaulay scheme to a regular scheme such that the second direct image does not vanish and has an isolated support. |
| title | On vanishing of higher direct images of the structure sheaf |
| topic | Algebraic Geometry Commutative Algebra 13H05, 13A30, 14B05 |
| url | https://arxiv.org/abs/2410.15282 |