$q$-bic threefolds and their surface of lines
Fuente:
arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866915840438304768 |
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| author | Cheng, Raymond |
| author_facet | Cheng, Raymond |
| contents | For any power $q$ of the positive ground field characteristic, a smooth $q$-bic threefold -- the Fermat threefold of degree $q+1$ for example -- has a smooth surface $S$ of lines which behaves like the Fano surface of a smooth cubic threefold. I develop projective, moduli-theoretic, and degeneration techniques to study the geometry of $S$. Using, in addition, the modular representation theory of the finite unitary group and the geometric theory of filtrations, I compute cohomology of the structure sheaf of $S$ when $q$ is prime. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_09884 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | $q$-bic threefolds and their surface of lines Cheng, Raymond Algebraic Geometry Number Theory Representation Theory 14F10, 14J29, 14G17, (primary), 14J70, 14M12, 14N05, (secondary) For any power $q$ of the positive ground field characteristic, a smooth $q$-bic threefold -- the Fermat threefold of degree $q+1$ for example -- has a smooth surface $S$ of lines which behaves like the Fano surface of a smooth cubic threefold. I develop projective, moduli-theoretic, and degeneration techniques to study the geometry of $S$. Using, in addition, the modular representation theory of the finite unitary group and the geometric theory of filtrations, I compute cohomology of the structure sheaf of $S$ when $q$ is prime. |
| title | $q$-bic threefolds and their surface of lines |
| topic | Algebraic Geometry Number Theory Representation Theory 14F10, 14J29, 14G17, (primary), 14J70, 14M12, 14N05, (secondary) |
| url | https://arxiv.org/abs/2402.09884 |