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Focal schemes to families of secant spaces to canonical curves. (arXiv:1710.01923v1 [math.AG])
来源于:arXiv
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 $\rho(g,d,1)=g-2(g-d+1)\geq 1$. 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 $1$. 查看全文>>