论文标题
尖光平滑曲线上的普遍模量堆栈的Picard组II
The Picard group of the universal moduli stack of principal bundles on pointed smooth curves II
论文作者
论文摘要
在本文中，这是Arxiv：2002.07494的续集，我们调查了任何还原性的$ g $，而不是代数封闭的字段$ k $，这是通用Moduli stack $ \ Mathrm {bunrm {bunrm {bunrm {bun} _ {g，g，g，g，g，g，g，g，g，g，n} $ g $ g $ -g $ $ n $ n $ n $ n $ n $ g $ g $ g $ g $ - 特别是：我们提供了$ \ mathrm {bun} _ {g，g，n} $的PICARD组的新功能演示；我们将限制同态在固定平滑曲线上的原理$ g $捆的模量堆栈的PICARD组中；我们按$ g $的中心确定$ \ mathrm {bun} _ {g，g，n} $的刚化的PICARD组以及相关GERBE的阻塞同构图像。结果，我们计算了可在$ n $ n $ $ n $ $ g $的$ n $ $ g $ of $ g $ $ g $的$ g $捆的模量空间的除数级组。
In this paper, which is a sequel of arXiv:2002.07494, we investigate, for any reductive group $G$ over an algebraically closed field $k$, the Picard group of the universal moduli stack $\mathrm{Bun}_{G,g,n}$ of $G$-bundles over $n$-pointed smooth projective curves of genus $g$. In particular: we give new functorial presentations of the Picard group of $\mathrm{Bun}_{G,g,n}$; we study the restriction homomorphism onto the Picard group of the moduli stack of principal $G$-bundles over a fixed smooth curve; we determine the Picard group of the rigidification of $\mathrm{Bun}_{G,g,n}$ by the center of $G$ as well as the image of the obstruction homomorphism of the associated gerbe. As a consequence, we compute the divisor class group of the moduli space of semistable $G$-bundles over $n$-pointed smooth projective curves of genus $g$.
