Principal 𝐺-bundles on Nodal Curves

Proceedings Mathematical Sciences

Usha N Bhosle¹ 

[1] School of Mathematics, Tata Institute of Fundamental Research, Homi Bhabha Road, Colaba, Mumbai 00 00, India$$

关键词: Principal bundles;    loop groups;    parabolic bundles.;   

DOI  :  

学科分类：数学（综合）

来源: Indian Academy of Sciences

【 摘 要 】

Let 𝐺 be a connected semisimple affine algebraic group defined over 𝐶. We study the relation between stable, semistable 𝐺-bundles on a nodal curve 𝑌 and representations of the fundamental group of 𝑌. This study is done by extending the notion of (generalized) parabolic vector bundles to principal 𝐺-bundles on the desingularization 𝐶 of 𝑌 and using the correspondence between them and principal 𝐺-bundles on 𝑌. We give an isomorphism of the stack of generalized parabolic bundles on 𝐶 with a quotient stack associated to loop groups. We show that if 𝐺 is simple and simply connected then the Picard group of the stack of principal 𝐺-bundles on 𝑌 is isomorphic to ⊕𝑚 𝑍, 𝑚 being the number of components of 𝑌.

【 授权许可】

Unknown