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On the stability of the universal quotient bundle restricted to congruences of low degree of G(1,3)

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
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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