Journal of the Korean Mathematical Society (대한수학회지)

Korean Mathematical Society (대한수학회)
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ON ENTIRE RATIONAL MAPS OF REAL SURFACES

  • Ozan, Yildiray (Middle East Technical University Department of Mathematics)
  • Published : 2002.01.01
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Abstract

In this paper, we define for a component $X_{0}$ of a nonsingular compact real algebraic surface X the complex genus of $X_{0}$, denoted by gc($X_{0}$), and use this to prove the nonexistence of nonzero degree entire rational maps f : $X_{0}$ Y provided that gc(Y) > gc($X_{0}$), analogously to the topological category. We construct connected real surfaces of arbitrary topological genus with zero complex genus.

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