Connections on real parabolic bundles over a real curve
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We give analogous criterion to admit a real parabolic con- nection 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 gcd(r, d) = 1 is real inde- composable if and only if it admits a real logarithmic connection singular exactly over one point with residue given as multiplication by − d r . We also give an equivalent condition for real indecomposable vector bundle in the case when real curve has no real points.
Abstract
We give analogous criterion to admit a real parabolic con- nection 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 gcd(r, d) = 1 is real inde- composable if and only if it admits a real logarithmic connection singular exactly over one point with residue given as multiplication by − d r . We also give an equivalent condition for real indecomposable vector bundle in the case when real curve has no real points.
참고문헌 (5)
- S. Amrutiya, "Real parabolic bundles over a real curve", Proc. Indian Acad. Sci. (Math. Sci.), 124, pp.17~30 (2014)
- M. F. Atiyah, "Complex analytic connections in fibre bundles", Trans. Amer. Math. Soc, 85, pp.181~207 (1957)
- I. Biswas, "A criterion for the existence of a flat connection on a parabolic vector bundle", Adv. Geom, 2(3), pp.231~241 (2002)
- W. Crawley-Boevey, "Indecomposable parabolic bundles and the existence of matrices in prescribed conjugacy class closures with product equal to the identity", Publ. Math. Inst. Hautes ´Etudes. Sci, 100, pp.171~207 (2004)
- A. Weil, "G´en´eralisation des fonctions ab´eliennes", J. Math. Pures Appl, 17, pp.47~87 (1938)