On the singular locus of Grassmann secant varieties

Cools, Filip

Bull. Belg. Math. Soc. Simon Stevin, Tome 16 (2009) no. 1, p. 799-803 / Harvested from Project Euclid

Résumé

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 $\text{Sing}(G_{h,k}(X))=G_{h,k-1}(X)$.

Détail

Publié le : 2009-12-15
Classification:  14M15,  14N05,  14H99