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S. Ruhallah Ahmadi Symmetries of K3 Surfaces
 

Summary: S. Ruhallah Ahmadi
Symmetries of K3 Surfaces:
Background Material
REGINA, OCTOBER 2010
SUPERVISOR: DR. B.C. GILLIGAN
ii
Contents
1 Introduction 1
1.1 Complex Manifold . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.1.1 Complex Projective Spaces . . . . . . . . . . . . . . . . . 2
1.1.2 Complex Tori . . . . . . . . . . . . . . . . . . . . . . . . 5
1.2 Blow Ups and Blow Downs . . . . . . . . . . . . . . . . . . . . . 6
1.3 Vector Bundles and Line Bundles . . . . . . . . . . . . . . . . . . 8
1.4 Line Bundles and Sheaf Cohomology . . . . . . . . . . . . . . . 9
1.5 Divisors and their corresponding Line Bundles . . . . . . . . . . 11
2 Covering spaces 13
2.1 Topological Covering . . . . . . . . . . . . . . . . . . . . . . . . 13
2.2 Complex structure on the covering space . . . . . . . . . . . . . . 15
2.2.1 Relation between 1(M) and covering of M . . . . . . . . 16
2.3 Universal Coverings . . . . . . . . . . . . . . . . . . . . . . . . . 16

  

Source: Argerami, Martin - Department of Mathematics and Statistics, University of Regina

 

Collections: Mathematics