Appendix to “Secant varieties and successive minima" by C. Soulé: On linear subspaces contained in the secant varieties of a projective curve
Author:
Claire Voisin
Journal:
J. Algebraic Geom. 13 (2004), 343-347
DOI:
https://doi.org/10.1090/S1056-3911-03-00354-0
Published electronically:
December 4, 2003
MathSciNet review:
2047702
Full-text PDF
Abstract |
References |
Additional Information
Abstract: We show that the $d$-th secant variety of a projective curve of genus $g$ imbedded in projective space by a complete linear system of degree $2g-2+m$, with $m$ at least $2d+3$, does not contain linear spaces of dimension bigger than $d-1$, and that the only linear subspaces of dimension $d-1$ contained in it are the obvious ones.
1 A. Bertram: Moduli of rank 2 vector bundles, theta divisors, and the geometry of curves in projective space, J. Diff. Geom. 35, 1992, 429-469.
1 A. Bertram: Moduli of rank 2 vector bundles, theta divisors, and the geometry of curves in projective space, J. Diff. Geom. 35, 1992, 429-469.
Additional Information
Claire Voisin
Affiliation:
Institut de Mathématiques de Jussieu, CNRS, UMR 7586, 175 rue du Chevaleret, 75013 Paris, France
MR Author ID:
237928
Email:
voisin@math.jussieu.fr
Received by editor(s):
November 20, 2001
Published electronically:
December 4, 2003