Article

Congruences on G(1,4) with split universal quotient bundle

Authors:
To read the full-text of this research, you can request a copy directly from the authors.

Abstract

This work provides a complete classification of the smooth three-folds in the Grassmann variety of lines in , for which the restriction of the universal quotient bundle is a direct sum of two line bundles. For this purpose we use the geometrical interpretation of the splitting of the quotient bundle as well as the meaning of the number of the independent global sections of each of its summands.

No full-text available

Request Full-text Paper PDF

To read the full-text of this research,
you can request a copy directly from the authors.

Article
Full-text available
In this survey we recognize Enrique Arrondo’s contributions over the whole of his career, recalling his professional history and collecting the results of his mathematical production.
Article
Full-text available
La memoria se divide en dos partes diferenciadas. En la primera, correspondiente al capítulo uno, se clasifican los fibrados sin cohomología intermedia de la Grassamanniana G(1,4) de las rectas de P4. A diferencia de lo que ocurre en la Grassamanniana de rectas P3, se obtienen familias infinitas de fibrados. Como paso particular de la clasificación se caracterizan cohomológicamente las sumas directas de fibrados trivales y fibrados universales de la Grassamanniana, Q, S y S (y sus twists). La segunda parte, dividida en dos capítulos (2 y 3), consiste en la clasificación de las subvariedades lisas y de dimensión tres de G(1,4), llamadas congruencias, que además verifican que el fibrado universal cociente, Q, restringido a ellas escinde en suma directa de fibrados no lineales. La clasificación se hace interpretando geométricamente tanto el significado que tiene esta escisión, como el del número de secciones globales independientes que tienen los correspondientes fibrados lineales
Article
Full-text available
We give a classification and a construction of all smooth (n1)(n-1)-dimensional varieties of lines in {\bf P}\sp n verifying that all their lines meet a curve. This also gives a complete classification of (n1)(n-1)-scrolls over a curve contained in G(1,n).
Article
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.
Article
We give the list of all possible congruences in G(1,4) of degree d ≤10 and we explicitely construct most of them.
Article
We classify those smooth (n-1)-folds in G(1,n) for which the restriction of the rank-(n-1) universal bundle has more than n+1 independent sections. As an aplication, we classify also those (n-1)-folds for which that bundle splits.
Article
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 P^{2n+1} to the Grassmannian of lines in P^{n+1}.
The universal rank-(n-1) bundles on G(1,n) restricted to subvarieties, collect Dedicado a la memoria de Fernando Serrano. [3] , Projections on Grassmannians of lines and characterization of Veronese varietes
  • E Arrondo
E. Arrondo, The universal rank-(n-1) bundles on G(1,n) restricted to subvarieties, collect. Math. 49 (1998), no. 2-3, 173–183, Dedicado a la memoria de Fernando Serrano. [3] , Projections on Grassmannians of lines and characterization of Veronese varietes, J.Algebraic Geom. 8 (1999), no. 50, 85–101.
3-scroll immersions in G(1,4)
  • Alzati
A. Alzati, 3-scroll immersions in G(1, 4), Ann. Univ. Ferrara 32 (1986), 45-54.
  • E Arrondo
  • M Bertolini
  • C Turrini
E. Arrondo, M. Bertolini, and C. Turrini, Classification of Smooth Congruences with a Fundamental Curve, Marcel Dekker (1994), no. 166, 43-56.
On congruences of lines in the projective space
  • Arrondo