Details
| Original language | English |
|---|---|
| Publication status | E-pub ahead of print - 15 Feb 2024 |
Abstract
Keywords
- math.AG, math.NT, math.RT, 14F10, 14J29, 14G17, (primary), 14J70, 14M12, 14N05, (secondary)
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2024.
Research output: Working paper/Preprint › Preprint
}
TY - UNPB
T1 - $q$-bic threefolds and their surface of lines
AU - Cheng, Raymond
N1 - 47 pages. Comments very welcome!
PY - 2024/2/15
Y1 - 2024/2/15
N2 - 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.
AB - 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.
KW - math.AG
KW - math.NT
KW - math.RT
KW - 14F10, 14J29, 14G17, (primary), 14J70, 14M12, 14N05, (secondary)
M3 - Preprint
BT - $q$-bic threefolds and their surface of lines
ER -