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On entire rational maps of real surfaces
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Abstract
In this paper, we define for a component X_0 of a nonsingularcompact real algebraic surface X the complex genus of X_0,denoted by g_{mathbb C}(X_0), and use this to prove thenonexistence of nonzero degree entire rational mapsf:X_0rightarrow Y provided that g_{mathbb C}(Y)> g_{mathbbC}(X_0), analogously to the topological category. We constructconnected real surfaces of arbitrary topological genus with zerocomplex genus.
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