School of Mathematics Colloquium
Relative holomorphic connections and moduli space of logarithmic connections singular over a finite subset of a compact Riemann surface.
by Dr. Anoop Singh (TIFR, Mumbai)
Thursday, November 5, 2020
from
to
(Asia/Kolkata)
at Over Zoom
at Over Zoom
Description |
Abstract : In this talk we discuss two problems. It is firstly about the relative holomorphic connections and we give a sufficient condition for the existence of relative holomorphic connections in a vector bundle over a complex analytic family of compact connected complex manifolds. we show that the relative Chern classes of a holomorphic vector bundle over a family of compact and K\"ahler manifolds vanish if the bundle admits a relative holomorphic connection. Secondly, we give a description of certain invariants of the moduli space of logarithmic connections singular over a finite subset of a compact Riemann surface with fixed residues. This moduli space is known to be quasi-projective variety. We compute the Picard group of the moduli space and show that the moduli space does not admit any non-constant algebraic functions, although it admits non-constant holomorphic functions. |