Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
9493274 | Journal of Algebra | 2005 | 8 Pages |
Abstract
Let Vn,dâPN, for N:=(n+dn)â1, be the order-d Veronese embedding of Pn, Xn,d:=T(Vn,d)âPN the tangent developable of Vn,d, and Ssâ1(Xn,d)âPN the s-secant variety of Xn,d, i.e. the closure in PN of the union of all (sâ1)-linear spaces spanned by s points of Xn,d. Ssâ1(Xn,d) has expected dimension min{N,(2n+1)sâ1}. Catalisano, Geramita, and Gimigliano conjectured that Ssâ1(Xn,d) has always the expected dimension, except when d=2, n⩾2s or d=3 and n=2,3,4. In this paper we prove their conjecture when n=2 and n=3.
Related Topics
Physical Sciences and Engineering
Mathematics
Algebra and Number Theory
Authors
E. Ballico,