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arXiv · 1807.09102

Genus 2 curves and generalized theta divisors

Sonia Brivio·Filippo F. Favale
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Abstract

In this paper we investigate generalized theta divisors $Θ_r$ in the moduli spaces $\mathcal{U}_C(r,r)$ of semistable vector bundles on a curve $C$ of genus $2$. We provide a desingularization $Φ$ of $Θ_r$ in terms of a projective bundle $π:\mathbb{P}(\mathcal{V})\to\mathcal{U}_C(r-1,r)$ which parametrizes extensions of stable vector bundles on the base by $\mathcal{O}_C$. Then, we study the composition of $Φ$ with the well known theta map $θ$. We prove that, when it is restricted to the general fiber of $π$, we obtain a linear embedding.

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BibTeXRIS

Sonia Brivio, Filippo F. Favale. 2019-05-14. Genus 2 curves and generalized theta divisors. https://doi.org/10.1016/j.bulsci.2019.05.002

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