### Impacto

Arrondo Esteban, Enrique and Graña Otero, Beatriz
(2006)
*Congruences on G(1,4) with split universal quotient bundle.*
Journal of Geometry and Physics, 56
(6).
pp. 1057-1067.
ISSN 0393-0440

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Official URL: http://www.sciencedirect.com/science/article/pii/S0393044005000999

## Abstract

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 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.

Item Type: | Article |
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Uncontrolled Keywords: | Grassmann varieties; quotient bundles; congruences |

Subjects: | Sciences > Mathematics > Algebraic geometry |

ID Code: | 14810 |

References: | [1] A. Alzati, 3-scroll immersions in G(1, 4), Ann. Univ. Ferrara 32 (1986) 45–54. [2] E. Arrondo, The universal rank-(n − 1) bundles on G(1, n) restricted to subvarieties, Collect. Math. 49 (2/3) (1998) 173–183, Dedicado a la memoria de Fernando Serrano. [3] E. Arrondo, Projections on Grassmannians of lines and characterization of Veronese varieties, J. Algebr. Geom. 8 (50) (1999) 85–101. [4] E. Arrondo, M. Bertolini, C. Turrini, Classification of Smooth Congruences with a Fundamental Curve, vol. 166, Marcel Dekker, 1994, pp. 43–56. [5] E. Arrondo, M. Bertolini, C. Turrini, Congruences of small degree inG(1, 4), Comm. Algebra 26 (10) (1998) 3249–3266. [6] E. Arrondo, M. Bertolini, C. Turrini, Quadric bundle congruences in G(1, n), Forum Math. 12 (2000) 649– 666. [7] E. Arrondo, I. Sols, On congruences of lines in the projective space,M´em. Soc. Math. France N.S. 50 (1992) 96. [8] B. Gra˜na, Escisi´on de fibrados en G(1, 4) y sus variedades, Ph.D. Thesis, Universidad Complutense de Madrid, January, 2003. [9] Z. Ran, Surfaces of order 1 in Grassmannians, J. Reine Angew. Math. 368 (1986) 119–126. |

Deposited On: | 18 Apr 2012 08:46 |

Last Modified: | 06 Feb 2014 10:09 |

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