Focal schemes to families of secant spaces to canonical curves

Michael Hoff

doi:10.1007/978-3-319-70566-8

paper

Focal schemes to families of secant spaces to canonical curves

arXiv:1710.01923 · doi:10.1007/978-3-319-70566-8

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 $d \leq g - 1$ 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 $P^{d - 2}$ 's to $C$ induced by the smooth locus of the Brill--Noether locus $W_{d}^{1} (C)$ . 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 $W_{d}^{1} (C)$ of dimension at least $1$ .

14 pages, to appear in: "Algorithmic and Experimental Methods in Algebra, Geometry, and Number Theory", DFG, SPP 1489

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Focal schemes to families of secant spaces to canonical curves

Abstract

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