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Moduli of K3 Surfaces and Complex Ball Quotients

Chapter
Part of the Progress in Mathematics book series (PM, volume 260)

Abstract

These notes are based on a series of talks given by the authors at the CIMPA Summer School on Algebraic Geometry and Hypergeometric Functions held in Istanbul in Summer of 2005. They provide an introduction to recent work on the complex ball uniformization of the moduli spaces of del Pezzo surfaces, K3 surfaces and algebraic curves of lower genus. We discuss the relationship of these constructions with the Deligne-Mostow theory of periods of hypergeometric differential forms. For convenience to a non-expert reader we include an introduction to the theory of periods of integrals on algebraic varieties with emphasis on abelian varieties and K3 surfaces.

Keywords

Hodge structure periods moduli Abelian varieties arrangements of hyperplanes K3 surfaces complex ball 

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Copyright information

© Birkhäuser Verlag Basel/Switzerland 2007

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of MichiganAnn ArborUSA
  2. 2.Graduate School of MathematicsNagoya UniversityNagoyaJapan

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