Stable bundles of rank 2 with 4 sections

Details Stable bundles of rank 2 with 4 sections Stable bundles of rank 2 with 4 sections

2010-06-07

arxiv.org/abs/1006.1258v3

Internat. J. Math. 22, no.12 (2011), 1743-1762

Mathematics

Algebraic Geometry

Correction of typos; introduction partially rewritten; postscript and new references added

Scientific paper

10.1142/S0129167X11007434

This paper contains results on stable bundles of rank 2 with space of sections of dimension 4 on a smooth irreducible projective algebraic curve $C$. There is a known lower bound on the degree for the existence of such bundles; the main result of the paper is a geometric criterion for this bound to be attained. For a general curve $C$ of genus 10, we show that the bound cannot be attained, but that there exist Petri curves of this genus for which the bound is sharp. We interpret the main results for various curves and in terms of Clifford indices and coherent systems.

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