ON FINITE BRANCHED UNIFORMIZATIONS OF THE PROJECTIVE PLANE


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ULUDAĞ A. M. , SARIOĞLU C. C.

INTERNATIONAL JOURNAL OF MATHEMATICS, vol.24, no.2, 2013 (Journal Indexed in SCI) identifier identifier

  • Publication Type: Article / Article
  • Volume: 24 Issue: 2
  • Publication Date: 2013
  • Doi Number: 10.1142/s0129167x13500171
  • Title of Journal : INTERNATIONAL JOURNAL OF MATHEMATICS

Abstract

We give a brief survey of the so-called Fenchel's problem for the projective plane, that is the problem of existence of finite Galois coverings of the complex projective plane branched along a given divisor and prove the following result: Let p, q be two integers greater than 1 and C be an irreducible plane curve. If there is a surjection of the fundamental group of the complement of C into a free product of cyclic groups of orders p and q, then there is a finite Galois covering of the projective plane branched along C with any given branching index.