Abstract
As we know from the Riemann-Roch theorem the topological classification of complex vector bundles E → M over compact Riemann surface is ‘very simple’: they are classified by one integer c 1(E), the first Chern class of E → M. The situation is quite different in the case of classification of holomorphic category. This could have been expected from our experience with the Teichmuller theory, the main chapter of the Riemann moduli problem.
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