• Principal Bundles whose Restrictions to a Curve are Isomorphic

• # Fulltext

https://www.ias.ac.in/article/fulltext/pmsc/121/02/0165-0170

• # Keywords

Vector bundle; very ample invertible sheaf; principal bundles; affine algebraic group; structure group; normal projective variety; Enrique–Severi; unipotent radical; reductive; parabolic subgroup.

• # Abstract

Let 𝑋 be a normal projective variety defined over an algebraically closed field 𝑘. Let $|O_X(1)|$ be a very ample invertible sheaf on 𝑋. Let 𝐺 be an affine algebraic group defined over 𝑘. Let $E_G$ and $F_G$ be two principal 𝐺-bundles on 𝑋. Then there exists an integer $n \gg 0$ (depending on $E_G$ and $F_G$) such that if the restrictions of $E_G$ and $F_G$ to a curve $C\in |O_X(n)|$ are isomorphic, then they are isomorphic on all of 𝑋.

• # Author Affiliations

1. School of Mathematics, Tata Institute of Fundamental Research, Dr Homi Bhabha Road, Mumbai 400 005, India

• # Proceedings – Mathematical Sciences

Volume 130, 2020
All articles
Continuous Article Publishing mode

• # Editorial Note on Continuous Article Publication

Posted on July 25, 2019