Stable rank three vector bundles without theta divisors over bielliptic curves

George H. Hitching

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arXiv · 1411.5353

Stable rank three vector bundles without theta divisors over bielliptic curves

George H. Hitching

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Abstract

Raynaud has shown that over a general curve of genus $g \ge 2$, every semistable bundle of rank three and integral slope admits a theta divisor. We show that this can fail for special curves: Over any bielliptic curve of genus $g \ge 5$, we construct a stable rank three bundle of trivial determinant with no theta divisor. This gives a partial answer to a question of Beauville.

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George H. Hitching. 2014-11-19. Stable rank three vector bundles without theta divisors over bielliptic curves. https://arxiv.org/abs/1411.5353

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