Información del autor
Autor Arrondo Esteban, Enrique |
Documentos disponibles escritos por este autor (38)
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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[...]texto impreso
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We provide an elementary proof of the Hartshorne-Serre correspondence for constructing vector bundles from local complete intersection subschemes of codimension two. This will be done, as in the correspondence of hypersurfaces and line bundles, [...]texto impreso
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In this work we introduce the definition of Schwarzenberger bundle on a Grassmannian. Recalling the notion of Steiner bundle, we generalize the concept of jumping pair for a Steiner bundle on a Grassmannian. After studying the jumping locus vari[...]texto impreso
A line congruence is an irreducible subvariety of dimension n?1 in the Grassmannian of lines in Pn. There are two numerical invariants associated to a line congruence: the order, which is the number of lines passing through a general point of Pn[...]texto impreso
Arrondo Esteban, Enrique ; Lanteri, Antonio ; Novelli, Carla | Department of Mathematics, Tokyo Institute of Technology | 2013A notion of "delta-genus" for ample vector bundles g of rank two on a smooth projective threefold X is defined as a couple of integers (delta(1),delta(2)).This extends the classical definition holding for ample line bundles. Then pairs (X, epsil[...]texto impreso
This well-written paper contains the thesis of Arrondo, written under the supervision of Sols. The topic is the study of smooth congruences (i.e. surfaces in the Grassmannian G=Gr(1,3) ), showing their parallelism with surfaces in P 4 . Th[...]texto impreso
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In this paper we study the normal bundle of the embedding of subvarieties of dimension n - 1 in the Grassmann variety of lines in P(n). Making use of some results on the geometry of the focal loci of congruences ([4] and [5]), we give some crite[...]texto impreso
We introduce a method to determine if n-dimensional smooth subvarieties of an ambient space of dimension at most 2n - 2 inherits the Picard group from the ambient space (as it happens when the ambient space is a projective space, according to re[...]texto impreso
We study the semistability of Q vertical bar s, the universal quotient bundle on G(1,3) restricted to any smooth surface S (called congruence). Specifically, we deduce geometric conditions for a congruence S, depending on the slope of a saturate[...]texto impreso
The purpose of this paper is to relate the variety parameterizing completely decomposable homogeneous polynomials of degree d in n + 1 variables on an algebraically closed field, called Split(d)(P(n)), with the Grassmannian of (n - 1)-dimensiona[...]texto impreso
In this paper we extend the classical notion of offset to the concept of generalized offset to hypersurfaces. In addition, we present a complete theoretical analysis of the rationality and unirationality of generalized offsets. Characterizations[...]texto impreso
We characterize the double Veronese embedding of P-n as the only variety that, under certain general conditions, can be isomorphically projected from the Grassmannian of lines in P2n+1 to the Grassmannian of lines in Pn+1.texto impreso
Arrondo Esteban, Enrique ; Mallavibarrena Martínez de Castro, Raquel ; Sols, Ignacio | Springer | 1990The purpose of the paper under review is to give a proof of six formulas by Schubert (two of which he proved and four of which he only conjectured) concerning the number of double contacts among the curves of two families of plane curves. The me[...]texto impreso
We give the list of all possible smooth congruences in G(1,n) which have a quadric bundle structure over a curve and we explicitely construct most of them.texto impreso
We introduce a generalized notion of Schwarzenberger bundle on the projective space. Associated to this more general definition, we give an ad hoc notion of jumping subspaces of a Steiner bundle on P(n) (which in rank n coincides with the notion[...]texto impreso
We prove that smooth subvarieties of codimension two in Grassmannians of lines of dimension at least six are rationally numerically subcanonical. We prove the same result for smooth quadrics of dimension at least six under some extra condition. [...]texto impreso
The author has, in several articles, studied varieties in the Grassmannian G(k, n) of kplanes in projective n-space, that are projections from a variety in G(k,N). In the case k = 1 the varieties of dimension n?1 in G(1, n) that are projections [...]texto impreso
A well known result of G. Horrocks [Proc. Lond. Math. Soc. (3) 14, 689-713 (1964; Zbl 0126.16801)] says that a vector bundle on a projective space has no intermediate cohomology if and only if it decomposes as a direct sum of line bundles. It is[...]texto impreso
It is a famous result due to G. Horrocks [Proc. Lond. Math. Soc. (3) 14, 689-713 (1964; Zbl 0126.16801)] that line bundles on a projective space are the only indecomposable vector bundles without intermediate cohomology. This fact generalizes to[...]texto impreso
We classify rank-2 vector bundles with no intermediate cohomology on the general prime Fano threefold of index 1 and genus 12. The structure of their moduli spaces is given by means of a monad-theoretic resolution in terms of exceptional bundles.