Theta divisors of stable vector bundles may be nonreduced

George H. Hitching; With an appendix by Christian Pauly

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arXiv · 1211.1064

Theta divisors of stable vector bundles may be nonreduced

George H. Hitching·With an appendix by Christian Pauly

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Abstract

A generic strictly semistable bundle of degree zero over a curve X has a reducible theta divisor, given by the sum of the theta divisors of the stable summands of the associated graded bundle. The converse is not true: Beauville and Raynaud have each constructed stable bundles with reducible theta divisors. For X of genus at least 5, we construct stable vector bundles over X of rank $r$ for all $r \geq 5$, with reducible and nonreduced theta divisors. We also adapt the construction to symplectic bundles. In the appendix, Raynaud's original example of a stable rank 2 vector bundle with reducible theta divisor over a bi-elliptic curve of genus 3 is generalized to bi-elliptic curves of genus $g \geq 3$.

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BibTeX RIS

George H. Hitching, With an appendix by Christian Pauly. 2013-06-08. Theta divisors of stable vector bundles may be nonreduced. https://arxiv.org/abs/1211.1064

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