Now showing items 1-3 of 3

• #### Criterion for logarithmic connections with prescribed residues ﻿

(2017-04-01)
A theorem of Weil and Atiyah says that a holomorphic vector bundle $E$ on a compact Riemann surface $X$ admits a holomorphic connection if and only if the degree of every direct summand of $E$ is zero. Fix a finite subset ...
• #### Local Topological Obstruction For Divisors ﻿

(2020)
Given a smooth, projective variety $X$ and an effective divisor $D\,\subseteq\, X$, it is well-known that the (topological) obstruction to the deformation of the fundamental class of $D$ as a Hodge class, lies in ...
• #### Logarithmic connections on principal bundles over a Riemann surface ﻿

(2017)
Let $E_G$ be a holomorphic principal $G$--bundle on a compact connected Riemann surface $X$, where $G$ is a connected reductive complex affine algebraic group. Fix a finite subset $D\, \subset\, X$, and for each \$x\,\in\, ...