In this paper we investigate generalized theta divisors ${\mathrm{\Theta }}_r$ 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 ${\mathrm{\Theta }}_r$ in terms of a projective bundle $\pi :\mathbb{P}(\mathcal{V})\to {\mathcal{U}}_C(r-1,r)$ 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.

中文翻译：

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属2曲线和广义theta除数

在本文中，我们研究了广义θ除数 ${\mathrm{\Theta }}_{\mathrm{[R}}$ 在模空间 ${\mathcal{ü}}_C（\mathrm{[R}，\mathrm{[R}）$属2的曲线C上的半稳定向量束。${\mathrm{\Theta }}_{\mathrm{[R}}$ 就射束而言 $\pi ：\mathbb{P}（\mathcal{V}）\to {\mathcal{ü}}_C（\mathrm{[R}-\mathrm{1个}，\mathrm{[R}）$ 它通过以下方式对稳定向量束的扩展进行参数化 ${\mathcal{Ø}}_C$。然后，我们用众所周知的θ图θ研究Φ的组成。我们证明，当将它限制在π的普通光纤上时，我们可以获得线性嵌入。