## Bulletin of the Belgian Mathematical Society - Simon Stevin

### On the singular locus of Grassmann secant varieties

Filip Cools

#### Abstract

Let $X\subset \mathbb{P}^N$ be an irreducible non-degenerate variety. If the $(h,k)$-Grass\-mann secant variety $G_{h,k}(X)$ of $X$ is not the whole Grassmannian $\mathbb{G}(h,N)$, we have that the singular locus of $G_{h,k}(X)$ contains $G_{h,k-1}(X)$. Moreover, if $X$ is a smooth curve without $(2k+2)$-secant $2k$-space divisors, we obtain the equality $\text{Sing}(G_{h,k}(X))=G_{h,k-1}(X)$.

#### Article information

Source
Bull. Belg. Math. Soc. Simon Stevin, Volume 16, Number 5 (2009), 799-803.

Dates
First available in Project Euclid: 9 December 2009

https://projecteuclid.org/euclid.bbms/1260369399

Digital Object Identifier
doi:10.36045/bbms/1260369399

Mathematical Reviews number (MathSciNet)
MR2574361

Zentralblatt MATH identifier
1181.14055

#### Citation

Cools, Filip. On the singular locus of Grassmann secant varieties. Bull. Belg. Math. Soc. Simon Stevin 16 (2009), no. 5, 799--803. doi:10.36045/bbms/1260369399. https://projecteuclid.org/euclid.bbms/1260369399