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Article Dans Une Revue Geometriae Dedicata Année : 2015

Theta divisors of stable vector bundles may be nonreduced

Résumé

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 $g \geq 3$.

Dates et versions

hal-00874716 , version 1 (18-10-2013)

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George H. Hitching, With an Appendix By Christian Pauly. Theta divisors of stable vector bundles may be nonreduced. Geometriae Dedicata, 2015, 177, pp.257-273. ⟨10.1007/s10711-014-9988-9⟩. ⟨hal-00874716⟩
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