Ebook: Ball and Surface Arithmetics

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.

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Inhalt

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Inhalt
Contents: Abelian Points - Orbital Curves - Orbital Surfaces - Ball Quotient Surfaces - Picard Modular Surfaces - Rationallyy Wighted Orbital Surfaces -

Zielgruppe
1. Mathematiker 2. Mathematik-Studenten h?herer Semester

?ber den Autor/Hrsg
Dr. Rolf-Peter Holzapfel ist Mitglied der Arbeitsgruppe "Allgebraische Geometrie und Zahlentheorie" am Max-Planck-Institut zur F?rderung der Wissenschaften, Berlin.
Content:
Front Matter....Pages i-xiii
Abelian Points....Pages 1-75
Orbital Curves....Pages 76-93
Orbital Surfaces....Pages 94-165
Ball Quotient Surfaces....Pages 166-258
Picard Modular Surfaces....Pages 259-299
Volumes of Fundamental Domains of Picard Modular Groups....Pages 300-329
?-Orbital Surfaces....Pages 330-400
Back Matter....Pages 401-414

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Inhalt
Contents: Abelian Points - Orbital Curves - Orbital Surfaces - Ball Quotient Surfaces - Picard Modular Surfaces - Rationallyy Wighted Orbital Surfaces -

Zielgruppe
1. Mathematiker 2. Mathematik-Studenten h?herer Semester

?ber den Autor/Hrsg
Dr. Rolf-Peter Holzapfel ist Mitglied der Arbeitsgruppe "Allgebraische Geometrie und Zahlentheorie" am Max-Planck-Institut zur F?rderung der Wissenschaften, Berlin.
Content:
Front Matter....Pages i-xiii
Abelian Points....Pages 1-75
Orbital Curves....Pages 76-93
Orbital Surfaces....Pages 94-165
Ball Quotient Surfaces....Pages 166-258
Picard Modular Surfaces....Pages 259-299
Volumes of Fundamental Domains of Picard Modular Groups....Pages 300-329
?-Orbital Surfaces....Pages 330-400
Back Matter....Pages 401-414
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