Ball and Surface Arithmetics

  • Rolf-Peter Holzapfel

Part of the Aspects of Mathematics book series (ASMA, volume 29)

Table of contents

  1. Front Matter
    Pages i-xiii
  2. Rolf-Peter Holzapfel
    Pages 1-75
  3. Rolf-Peter Holzapfel
    Pages 76-93
  4. Rolf-Peter Holzapfel
    Pages 94-165
  5. Rolf-Peter Holzapfel
    Pages 166-258
  6. Rolf-Peter Holzapfel
    Pages 259-299
  7. Rolf-Peter Holzapfel
    Pages 300-329
  8. Rolf-Peter Holzapfel
    Pages 330-400
  9. Back Matter
    Pages 401-414

About this book

Introduction

This monograph is based on the work of the author on surface theory con­ nected with ball uniformizations and arithmetic ball lattices during several years appearing in a lot of special articles. The first four chapters present the heart of this work in a self-contained manner (up to well-known ba­ sic facts) increased by the new functorial concept of orbital heights living on orbital surfaces. It is extended in chapter 6 to an explicit HURWITZ theory for CHERN numbers of complex algebraic surfaces with the mildest singularities, which are necessary for general application and proofs. The chapter 5 is dedicated to the application of results in earlier chapters to rough and fine classifications of PICARD modular surfaces. For this part we need additionally the arithmetic work of FEUSTEL whose final results are presented without proofs but with complete references. We had help­ ful connections with Russian mathematicians around VENKOV, VINBERG, MANIN, SHAFAREVICH and the nice guide line of investigations of HILBERT modular surfaces started by HIRZEBRUCH in Bonn. More recently, we can refer to the independent (until now) study of Zeta functions of PICARD modular surfaces in the book [L-R] edited by LANGLANDS and RAMAKR­ ISHN AN. The basic idea of introducing arrangements on surfaces comes from the monograph [BHH], (BARTHEL, HOFER, HIRZEBRUCH) where linear ar­ rangements on the complex projective plane ]p2 play the main role.

Keywords

algebra algorithms classification field manifold quality structure surface surfaces

Authors and affiliations

  • Rolf-Peter Holzapfel
    • 1
  1. 1.Mathematisch-Naturwissenschaftliche Fakultät II, Institut für MathematikHumboldt-Universität BerlinBerlinGermany

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-322-90169-9
  • Copyright Information Vieweg+Teubner Verlag | Springer Fachmedien Wiesbaden GmbH, Wiesbaden 1998
  • Publisher Name Vieweg+Teubner Verlag
  • eBook Packages Springer Book Archive
  • Print ISBN 978-3-322-90171-2
  • Online ISBN 978-3-322-90169-9
  • Series Print ISSN 0179-2156
  • About this book