曲线上向量丛模空间乘积的Torelli定理

中文摘要 AI 辅助

我们证明了在亏格$g\\,\ge\\, 4$的光滑射影曲线上，半稳定向量丛的模空间的乘积满足Torelli型定理。对于半稳定向量丛的模叠的乘积，我们也证明了类似的结果。该证明利用了Picard秩为一且Picard群离散的正规射影簇乘积的分解定理。作为应用，我们计算了模空间和模叠乘积的自同构群。

英文摘要

We prove a Torelli-type theorem for a product of the moduli spaces of semistable vector bundles over smooth projective curves of genus $g\,\ge\, 4$. A similar result is proved for the product of the moduli stacks of semistable vector bundles. This is proved using a decomposition theorem for the product of the normal projective varieties with Picard rank one and discrete Picard group. As an application, we compute the automorphism group of the product of the moduli spaces and moduli stacks.

发表机构

• Shiv Nadar University（希夫纳德大学）
• IIT Madras（印度理工学院马德拉斯分校）

机构由 AI 辅助整理，请以论文原文为准。