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- W1502154118 abstract "The geometry of the Fano scheme of maximal linear spaces contained in the base locus of a pencil of quadrics has been studied by algebraic geometers when the base field is algebraically closed. In this paper, we work over an arbitrary base field of characteristic not equal to 2 and show how these Fano schemes are related to the Jacobians of hyperelliptic curves. In particular, if $B$ is the base locus of a generic pencil of quadrics in $bbp^{2n+1}$, and $F$ is the Fano variety of $n - 1$ planes contained in $B$, then $F$ is a component of a disconnected commutative algebraic group $G = picz(C) dcup F dcup pico(C) dcup F'$, where $C$ is the hyperelliptic curve defined by the discriminant form of the pencil. In the second half of this paper, we study regular pencils of quadrics, where the hyperelliptic curve defined by the discriminant is singular." @default.
- W1502154118 created "2016-06-24" @default.
- W1502154118 creator A5054328347 @default.
- W1502154118 date "2013-02-10" @default.
- W1502154118 modified "2023-09-25" @default.
- W1502154118 title "Maximal linear spaces contained in the base loci of pencils of quadrics" @default.
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- W1502154118 doi "https://doi.org/10.48550/arxiv.1302.2385" @default.
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