Automorphic factors of degree n of a compact complex manifold are defined and the problem that « Can every automorphic factor of degree n over a compact Riemann surface M be expressed as a product of a representation of the fundamental group of M and a certain canonical automorphic factor of M? » is studied. The answer is found in affirmative for factors of degree1 and in negative for higher degree factors by explicit construction.
Riemann Surface Fundamental Group Complex Manifold Explicit Construction Compact Riemann Surface
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