Galois coverings of the plane by K3 surfaces

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Uludag A.

KYUSHU JOURNAL OF MATHEMATICS, cilt.59, sa.2, ss.393-419, 2005 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 59 Sayı: 2
  • Basım Tarihi: 2005
  • Doi Numarası: 10.2206/kyushujm.59.393
  • Dergi Adı: KYUSHU JOURNAL OF MATHEMATICS
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Aerospace Database, MathSciNet, zbMATH, Civil Engineering Abstracts
  • Sayfa Sayıları: ss.393-419
  • Anahtar Kelimeler: K3 surface, groups acting on a K3 surface, orbifold, uniformization, branched Galois covering
  • Galatasaray Üniversitesi Adresli: Evet

Özet

We study branched Galois coverings of the projective plane by smooth K3 surfaces. Branching data of such a covering determines in a unique way a uniformizable orbifold on the plane. In order to study Galois coverings of the plane by K3 surfaces, it suffices to study orbifolds on the plane uniformized by K3 surfaces. We call these K3 orbifolds and classify K3 orbifolds with an abelian uniformization. We also classify K3 orbifolds with a locus of degree less than 6 and with a non-abelian uniformization. There are no K3 orbifolds with a locus of degree greater than 6. Although we give some examples of K3 orbifolds with a sextic locus, our results are incomplete in this case.