Focal Schemes to Families of Secant Spaces to Canonical Curves

Michael Hoff ()
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Michael Hoff: Universität des Saarlandes

A chapter in Algorithmic and Experimental Methods in Algebra, Geometry, and Number Theory, 2017, pp 387-401 from Springer

Abstract: Abstract For a general canonically embedded curve C of genus g ≥ 5, let d ≤ g − 1 be an integer such that the Brill–Noether number ρ(g, d, 1) = g − 2(g − d + 1) ≥ 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 ) $$W^1_d(C)$$ . 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 d 1 ( C ) $$W^1_d(C)$$ of dimension at least 1.

Keywords: Focal scheme; Brill-Noether locus; Torelli-type theorem; 14H51; 14M12; 14C34 (search for similar items in EconPapers)
Date: 2017
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-319-70566-8_15

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DOI: 10.1007/978-3-319-70566-8_15

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