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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


Appell Hypergeometric Functions

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/9780691144771.003.0008
Subject:
Mathematics, Geometry / Topology

This chapter discusses the complete quadrilateral line arrangement, and especially its relationship with the space of regular points of the system of partial differential equations defining the ... 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


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


Spectral Sequences

Loring W. Tu

in Introductory Lectures on Equivariant Cohomology: (AMS-204)

Published in print:
2020
Published Online:
January 2021
ISBN:
9780691191751
eISBN:
9780691197487
Item type:
chapter
Publisher:
Princeton University Press
DOI:
10.23943/princeton/9780691191751.003.0006
Subject:
Mathematics, Educational Mathematics

This chapter focuses on spectral sequences. The spectral sequence is a powerful computational tool in the theory of fiber bundles. First introduced by Jean Leray in the 1940s, it was further refined ... More


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