| 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.
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