Search results for "Grassmannians"

Subvarieties of the Grassmannian $G(1,N)$ with small secant variety

2002

Classification of n-dimensional subvarieties of G(1, 2n) that can be projected to G(1, n + 1)

2005

A structure theorem is given for n-dimensional smooth subvarieties of the Grassmannian G(1, N); with N >= n + 3, that can be isomorphically projected to G(1, n + 1). A complete classification in the cases N = 2n + 1 and N = 2n follows, as a corollary.

Projecting 4-folds from G(1, 5) to G(1, 4)

2002

We study 4-dimensional subvarieties of the Grassmannian G(1,5) with singular locus of dimension at most 1 that can be isomorphically projected to G(1,4).

On globally generated vector bundles on projective spaces

2009

AbstractA classification is given for globally generated vector bundles E of rank k on Pn having first Chern class c1(E)=2. In particular, we get that they split if k<n unless E is a twisted null-correlation bundle on P3. In view of the well-known correspondence between globally generated vector bundles and maps to Grassmannians, we obtain, as a corollary, a classification of double Veronese embeddings of Pn into a Grassmannian G(k−1,N) of (k−1)-planes in PN.

On double Veronese embeddings in the Grassmannian G(1,N)

2004

We classify all the embeddings of P^n in a Grassmannian of lines G(1,N) such that the composition with Pl\"ucker is given by a linear system of quadrics of P^n.

The Coble Quadric

2023

Given a smooth genus three curve $C$, the moduli space of rank two stable vector bundles on C with trivial determinant embeds in $\mathbb{P}^8$ as a hypersurface whose singular locus is the Kummer threefold of $C$; this hypersurface is the Coble quartic. Gruson, Sam and Weyman realized that this quartic could be constructed from a general skew-symmetric fourform in eight variables. Using the lines contained in the quartic, we prove that a similar construction allows to recover SU$_C(2, L)$, the moduli space of rank two stable vector bundles on C with fixed determinant of odd degree L, as a subvariety of $G(2, 8)$. In fact, each point $p \in C$ defines a natural embedding of SU$_C(2, \mathca…