Generalization of a criterion for semistable vector bundles

Biswas, Indranil ; Hein, Georg (2009) Generalization of a criterion for semistable vector bundles Finite Fields and Their Applications, 15 (5). pp. 580-584. ISSN 1071-5797

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Official URL: http://linkinghub.elsevier.com/retrieve/pii/S10715...

Related URL: http://dx.doi.org/10.1016/j.ffa.2009.06.001

Abstract

It is known that a vector bundle E on a smooth projective curve Y defined over an algebraically closed field is semistable if and only if there is a vector bundle F on Y such that both H0(X,E⊗ F) and H1(X,E⊗F) vanishes. We extend this criterion for semistability to vector bundles on curves defined over perfect fields. Let X be a geometrically irreducible smooth projective curve defined over a perfect field k, and let E be a vector bundle on X. We prove that E is semistable if and only if there is a vector bundle F on X such that Hi(X,E⊗F)=0 for all i. We also give an explicit bound for the rank of F.

Item Type:Article
Source:Copyright of this article belongs to Elsevier Science.
Keywords:Moduli Space; Vector Bundles on a Curve; Generalized Theta Divisor
ID Code:3549
Deposited On:12 Oct 2010 04:16
Last Modified:12 Oct 2010 04:16

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