ON FINITE BRANCHED UNIFORMIZATIONS OF THE PROJECTIVE PLANE

ULUDAĞ A. M., SARIOĞLU C. C.

INTERNATIONAL JOURNAL OF MATHEMATICS, cilt.24, sa.2, 2013 (SCI-Expanded) identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 24 Sayı: 2
  • Basım Tarihi: 2013
  • Doi Numarası: 10.1142/s0129167x13500171
  • Dergi Adı: INTERNATIONAL JOURNAL OF MATHEMATICS
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Anahtar Kelimeler: Fenchel problem, uniformization, branched covering, generalized triangle group, COVERINGS, ORBIFOLDS, S3
  • Dokuz Eylül Üniversitesi Adresli: Evet

Özet

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.