548 research outputs found
The Grassmann Space of a Planar Space
AbstractIn this paper we give a characterization of the Grassmann space of a planar space
The Degree of the Tangent and Secant Variety to a Projective Surface
In this paper we present a way of computing the degree of the secant (resp.,
tangent) variety of a smooth projective surface, under the assumption that the
divisor giving the embedding in the projective space is -very ample. This
method exploits the link between these varieties and the Hilbert scheme
-dimensional subschemes of length of the surface.Comment: 20 pages; generalization of the previous version (from projective K3
surfaces to any projective surface) and improvement of the expositio
On the Grassmann space representing the lines of an affine space
AbstractIn 1982, Bichara and Mazzocca characterized the Grassmann space Gr(1,A) of the lines of an affine space A of dimension at least 3 over a skew-field K by means of the intersection properties of the three disjoint families Σ1,Σ2 and T of maximal singular subspaces of Gr(1,A). In this paper, we deal with the characterization of Gr(1,A) using only the family Σ=Σ1∪Σ2 of maximal singular subspaces
Orbital degeneracy loci and applications
Degeneracy loci of morphisms between vector bundles have been used in a wide
variety of situations. We introduce a vast generalization of this notion, based
on orbit closures of algebraic groups in their linear representations. A
preferred class of our orbital degeneracy loci is characterized by a certain
crepancy condition on the orbit closure, that allows to get some control on the
canonical sheaf. This condition is fulfilled for Richardson nilpotent orbits,
and also for partially decomposable skew-symmetric three-forms in six
variables. In order to illustrate the efficiency and flexibility of our
methods, we construct in both situations many Calabi--Yau manifolds of
dimension three and four, as well as a few Fano varieties, including some new
Fano fourfolds.Comment: To appear in Ann. Sc. Norm. Super. Pisa Cl. Sci. (5
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