Exact Sequence of Stable Vector Bundles on Projective Curves | Zendy

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Exact Sequence of Stable Vector Bundles on Projective Curves

Author(s) -

Ballico Edoardo,

Brambila Leticia,

Russo Barbara

Publication year - 1998

Publication title -

mathematische nachrichten

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.913

H-Index - 50

eISSN - 1522-2616

pISSN - 0025-584X

DOI - 10.1002/mana.19981940102

Subject(s) - mathematics , rank (graph theory) , algebraically closed field , vector bundle , genus , conjecture , image (mathematics) , exact sequence , combinatorics , extension (predicate logic) , pure mathematics , projective line , field (mathematics) , projective test , projective space , biology , botany , artificial intelligence , computer science , programming language

Let X be a smooth complex projective curve of genus g over an algebraically closed field k of charcteristic 0. In this paper we prove that given two general stable bundles F and G such thatthere exists an extensionof G by F with E stable. Moreover, such extension also exists for any general stable bundles of F and G of degree even and X either a double covering of a curve of genus 2 or a curve of genus g ≥ 3 + 4(rank G + rank F ) + max {rank G , rank F ). That solves Lange's conjecture ([L2], p. 455) for such cases.

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