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We introduce the notion of Pfaffian linkage in codimension three and give sufficient conditions for the linked variety to be smooth. As a result, we are able to construct smooth congruences of lines in P-4 whose existence was an open problem.texto impreso
The aim of this note is to prove some bounds on the global sections of vector bundles over a smooth, complete and connected curve C . Just by an application of the Clifford theorem, the authors prove (Proposition 2) (*) h 0 (E)?deg(E)/2+2 for a[...]texto impreso
Let G(r,m) denote the Grassmann variety of r-dimensional linear subspaces of Pm. To any linear projection Pm?Pm?, m?texto impreso
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 cor[...]texto impreso
We give a complete classification of smooth congruences - i.e. surfaces in the Grassmann variety of lines in P 3C identified with a smooth quadric in P5- of degree at most 8, by studying which surfaces of P5can lie in a smooth quadric and provin[...]texto impreso
A congruence of lines is a (n?1)-dimensional family of lines in Pn (over C), i.e. a variety Y of dimension (and hence of codimension) n ? 1 in the Grassmannian Gr(1, Pn). A fundamental curve for Y is a curve C Pn which meets all the lines of Y [...]texto impreso
We introduce a notion of regularity for coherent sheaves on Grassmannians of lines. We use this notion to prove some extension of Evans-Griffith criterion to characterize direct sums of line bundles. We also give. in the line of previous results[...]texto impreso
We give the list of all possible congruences in G(1,4) of degree d less than or equal to 10 and we explicitely construct most of them.texto impreso
This work provides a complete classification of the smooth three-folds in the Grassmann variety of lines in P-4, for which the restriction of the universal quotient bundle is a direct sum of two line bundles. For this purpose we use the geometri[...]texto impreso
In this paper we study arithmetically Cohen-Macaulay (ACM for short) vector bundles E of rank k 3 on hypersurfaces Xr P4 of degree r 1. We consider here mainly the case of degree r = 4, which is the first unknown case in literature. Under som[...]texto impreso
In this paper, we show that any smooth subvariety of codimension two in G(1,4) (the Grassmannian of lines of P-4) of degree at most 25 is subcanonical. Analogously, we prove that smooth subvarieties of codimension two in G(1,4) that are not of g[...]texto impreso
We introduce the different focal loci (focal points, planes and hyperplanes) of (n - 1)-dimensional families (congruences) of lines in P-n and study their invariants, geometry and the relation among them. We also study some particular congruence[...]texto impreso
Congruences of lines in P3, i.e. two-dimensional families of lines, and their focal surfaces, have been a popular object of study in classical algebraic geometry. They have been considered recently by several authors as Arrondo, Goldstein, Sols,[...]texto impreso
Arrondo Esteban, Enrique ; Sendra, Juana ; Sendra, J. Rafael | Elsevier Science B.V. (North-Holland) | 1999In this paper, we present a formula for computing the genus of irreducible generalized offset curves to projective irreducible plane curves with only affine ordinary singularities over an algebraically closed field. The formula expresses the gen[...]
