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Keywords:

  • Real curve;
  • linear pencil;
  • topological degree;
  • morphism;
  • Brill-Noether Theory;
  • divisor MSC (2010) 14H51;
  • 14P99

Abstract

We consider coverings of real algebraic curves to real rational algebraic curves. We show the existence of such coverings having prescribed topological degree on the real locus. From those existence results we prove some results on Brill-Noether Theory for pencils on real curves. For coverings having topological degree equation image we introduce the covering number k and we prove the existence of coverings of degree 4 with prescribed covering number.