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arXiv · 1710.01923

Focal schemes to families of secant spaces to canonical curves

Michael Hoff
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Abstract

This article is a generalisation of results of Ciliberto and Sernesi. For a general canonically embedded curve $C$ of genus $g\geq 5$, let $d\le g-1$ be an integer such that the Brill--Noether number $ρ(g,d,1)=g-2(g-d+1)\geq 1$. We study the family of $d$-secant $\mathbb{P}^{d-2}$'s to $C$ induced by the smooth locus of the Brill--Noether locus $W^1_d(C)$. Using the theory of foci and a structure theorem for the rank one locus of special $1$-generic matrices by Eisenbud and Harris, we prove a Torelli-type theorem for general curves by reconstructing the curve from its Brill--Noether loci $W^1_d(C)$ of dimension at least $1$.

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Michael Hoff. 2017-10-05. Focal schemes to families of secant spaces to canonical curves. https://doi.org/10.1007/978-3-319-70566-8

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