This communication is devoted to the generalization of two classical results in the theory of Riemann surfaces to the setting of SUSY-curves: 1. any holomorphic line bundle over a compact Riemann surface with vanishing Chern class is isomorphic to a flat bundle (the trasposition of this result to SUSY-curves requires the introduction of the notions of relative bundle, relative Chern class, and relatively flat bundles); 2. the Chern-Weil theorem for SUSY curves.
Some results on line bundles over SUSY-curves
BARTOCCI, CLAUDIO;
1990-01-01
Abstract
This communication is devoted to the generalization of two classical results in the theory of Riemann surfaces to the setting of SUSY-curves: 1. any holomorphic line bundle over a compact Riemann surface with vanishing Chern class is isomorphic to a flat bundle (the trasposition of this result to SUSY-curves requires the introduction of the notions of relative bundle, relative Chern class, and relatively flat bundles); 2. the Chern-Weil theorem for SUSY curves.
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