Arrondo Esteban, Enrique and Cobo Pablos, Sofía
(2010)
*On the stability of the universal quotient bundle restricted to congruences of low degree of G(1,3).*
Annali Della Scuola Normale Superiore Di Pisa-Classe Di Scienze, 93
.
pp. 503-522.
ISSN 0391-173X

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## Abstract

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 saturated linear subsheaf of Q vertical bar s. Moreover, we check that the Dolgachev-Reider Conjecture (i.e. the semistability of Q vertical bar s for nondegenerate congruences S) is true for all the congruences of degree less than or equal to 10. Also, when the degree of a congruence S is less than or equal to 9, we compute the highest slope reached by the linear subsheaves of Q vertical bar s.

Item Type: | Article |
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Uncontrolled Keywords: | Smooth surfaces; Lines |

Subjects: | Sciences > Mathematics > Algebraic geometry |

ID Code: | 14755 |

Deposited On: | 17 Apr 2012 11:34 |

Last Modified: | 06 Feb 2014 10:08 |

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