Connections on real parabolic bundles over a real curve
Bull. Korean Math. Soc. 2014 Vol. 51, No. 4, 1101-1113
Printed July 31, 2014
Sanjay Amrutiya
CIT Campus
Abstract : We give analogous criterion to admit a real parabolic connection on real parabolic bundles over a real curve. As an application of this criterion, if real curve has a real point, then we proved that a real vector bundle $E$ of rank $r$ and degree $d$ with $\mathrm{gcd}(r, d) = 1$ is real indecomposable if and only if it admits a real logarithmic connection singular exactly over one point with residue given as multiplication by $-\frac{d}{r}$. We also give an equivalent condition for real indecomposable vector bundle in the case when real curve has no real points.
Keywords : real parabolic bundles, real holomorphic connection, real curve
MSC numbers : Primary 14H60, 14P99; Secondary 14E20
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