## Bulletin of the Belgian Mathematical Society - Simon Stevin

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

#### Abstract

In this note we consider multiples $aD$, where $D$ is a divisor of the blow-up of $\mathbb{P}^n$ 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 $h^1(X,2D) = 0$.

#### Article information

Source
Bull. Belg. Math. Soc. Simon Stevin, Volume 16, Number 5 (2009), 933-942.

Dates
First available in Project Euclid: 9 December 2009

Permanent link to this document
https://projecteuclid.org/euclid.bbms/1260369407

Digital Object Identifier
doi:10.36045/bbms/1260369407

Mathematical Reviews number (MathSciNet)
MR2574370

Zentralblatt MATH identifier
1186.14009

Subjects
Primary: 14C20: Divisors, linear systems, invertible sheaves

Keywords
Linear systems fat points

#### Citation

Laface, Antonio; Ugaglia, Luca. On multiples of divisors associated to Veronese embeddings with defective secant variety. Bull. Belg. Math. Soc. Simon Stevin 16 (2009), no. 5, 933--942. doi:10.36045/bbms/1260369407. https://projecteuclid.org/euclid.bbms/1260369407