论文信息 - On multiples of divisors associated to Veronese embeddings with defective secant variety

On multiples of divisors associated to Veronese embeddings with defective secant variety

In this note we consider multiples aD, where D is a divisor of the blow-up of P^n along points in general position which appears in the Alexander and Hirschowitz list of Veronese embeddings having defective secant varieties. In particular we show that there is such a D with h^1(X,D) > 0 and h^1(X,2D) = 0.

A. Laface | L. Ugaglia

[1] A. Laface,et al. On a class of special linear systems of $\mathbb{P}^3$ , 2006 .

[2] Stephanie Yang. Linear series in P^2 with base points of bounded multiplicity , 2004 .

[3] A. Laface,et al. On a class of special linear systems of P^3 , 2003, math/0311445.

[4] A. Laface,et al. Linear systems on generic $K3$ surfaces , 2003, math/0309073.

[5] K. Chandler. A brief proof of a maximal rank theorem for generic double points in projective space , 2000 .

[6] Tomas Sauer,et al. Polynomial interpolation in several variables , 2000, Adv. Comput. Math..

[7] C. Ciliberto,et al. Degenerations of Planar Linear Systems , 1997, alg-geom/9702015.

[8] C. D. Boor,et al. Polynomial interpolation in several variables , 1994 .

[9] T. Willmore. Algebraic Geometry , 1973, Nature.

[10] Evgueni A. A. Tevelev,et al. Projective Duality and Homogeneous Spaces , 2005 .

[11] Rick Miranda,et al. LINEAR SYSTEMS OF PLANE CURVES , 1999 .

[12] A. Hirschowitz,et al. HYPERCUBIQUES DE P4 AVEC SEPT POINTS SINGULIERS GENERIQUES , 1991 .

[13] André Hirschowitz,et al. Une conjecture pour la cohomologie des diviseurs sur les surfaces rationelles génériques. , 1989 .

[14] Brian Harbourne,et al. THE GEOMETRY OF RATIONAL SURFACES AND HILBERT FUNCTIONS OF POINTS IN THE PLANE , 1986 .