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Algebraic Surfaces and the Miyaoka-Yau Inequality

Paula Tretkoff

in Complex Ball Quotients and Line Arrangements in the Projective Plane (MN-51)

Published in print:
2016
Published Online:
October 2017
ISBN:
9780691144771
eISBN:
9781400881253
Item type:
chapter
Publisher:
Princeton University Press
DOI:
10.23943/princeton/9780691144771.003.0005
Subject:
Mathematics, Geometry / Topology

This chapter discusses complex algebraic surfaces, with particular emphasis on the Miyaoka-Yau inequality and the rough classification of surfaces. Every complex algebraic surface is birationally ... More


Complex Surfaces and Coverings

Paula Tretkoff

in Complex Ball Quotients and Line Arrangements in the Projective Plane (MN-51)

Published in print:
2016
Published Online:
October 2017
ISBN:
9780691144771
eISBN:
9781400881253
Item type:
chapter
Publisher:
Princeton University Press
DOI:
10.23943/princeton/9780691144771.003.0004
Subject:
Mathematics, Geometry / Topology

This chapter deals with complex surfaces and their finite coverings branched along divisors, that is, subvarieties of codimension 1. In particular, it considers coverings branched over transversally ... More


Introduction

Paula Tretkoff

in Complex Ball Quotients and Line Arrangements in the Projective Plane (MN-51)

Published in print:
2016
Published Online:
October 2017
ISBN:
9780691144771
eISBN:
9781400881253
Item type:
chapter
Publisher:
Princeton University Press
DOI:
10.23943/princeton/9780691144771.003.0001
Subject:
Mathematics, Geometry / Topology

This chapter explains that the book deals with quotients of the complex 2-ball yielding finite coverings of the projective plane branched along certain line arrangements. It gives a complete list of ... More


Complex Ball Quotients and Line Arrangements in the Projective Plane (MN-51)

Paula Tretkoff

Published in print:
2016
Published Online:
October 2017
ISBN:
9780691144771
eISBN:
9781400881253
Item type:
book
Publisher:
Princeton University Press
DOI:
10.23943/princeton/9780691144771.001.0001
Subject:
Mathematics, Geometry / Topology

This book introduces the theory of complex surfaces through a comprehensive look at finite covers of the projective plane branched along line arrangements. It emphasizes those finite coverings that ... More


Line Arrangements in P2(C) and Their Finite Covers

Paula Tretkoff

in Complex Ball Quotients and Line Arrangements in the Projective Plane (MN-51)

Published in print:
2016
Published Online:
October 2017
ISBN:
9780691144771
eISBN:
9781400881253
Item type:
chapter
Publisher:
Princeton University Press
DOI:
10.23943/princeton/9780691144771.003.0006
Subject:
Mathematics, Geometry / Topology

This chapter discusses the free 2-ball quotients arising as finite covers of the projective plane branched along line arrangements. It first considers a surface X obtained by blowing up the singular ... More


Dynamics of automorphisms of compact complex surfaces

Serge Cantat

Araceli Bonifant, Mikhail Lyubich, and Scott Sutherland (eds)

in Frontiers in Complex Dynamics: In Celebration of John Milnor's 80th Birthday

Published in print:
2014
Published Online:
October 2017
ISBN:
9780691159294
eISBN:
9781400851317
Item type:
chapter
Publisher:
Princeton University Press
DOI:
10.23943/princeton/9780691159294.003.0018
Subject:
Mathematics, Combinatorics / Graph Theory / Discrete Mathematics

This chapter describes the dynamics of automorphisms of compact complex surfaces when it is rich. In particular, the chapter carries to this general setting the interplay between ideas from ergodic ... More


Complex surfaces

Selman Akbulut

in 4-Manifolds

Published in print:
2016
Published Online:
November 2016
ISBN:
9780198784869
eISBN:
9780191827136
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198784869.003.0012
Subject:
Mathematics, Geometry / Topology

Handlebody of Milnor fibers, complex surfaces, Blowing up singularities


Entropy for hyperbolic Riemann surface laminations II

Tien-Cuong Dinh, Viet-Anh Nguyen, and Nessim Sibony

Araceli Bonifant, Mikhail Lyubich, and Scott Sutherland (eds)

in Frontiers in Complex Dynamics: In Celebration of John Milnor's 80th Birthday

Published in print:
2014
Published Online:
October 2017
ISBN:
9780691159294
eISBN:
9781400851317
Item type:
chapter
Publisher:
Princeton University Press
DOI:
10.23943/princeton/9780691159294.003.0021
Subject:
Mathematics, Combinatorics / Graph Theory / Discrete Mathematics

This chapter studies Riemann surface foliations with tame singular points. It shows that the hyperbolic entropy of a Brody hyperbolic foliation by Riemann surfaces with linearizable isolated ... More


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