with an appendix by Bernard Teissier
Translated by Ben Lichtin
Softcover ISBN:  9780821829837 
Product Code:  ULECT/39 
List Price:  $69.00 
MAA Member Price:  $62.10 
AMS Member Price:  $55.20 
eBook ISBN:  9781470421830 
Product Code:  ULECT/39.E 
List Price:  $65.00 
MAA Member Price:  $58.50 
AMS Member Price:  $52.00 
Softcover ISBN:  9780821829837 
eBook: ISBN:  9781470421830 
Product Code:  ULECT/39.B 
List Price:  $134.00 $101.50 
MAA Member Price:  $120.60 $91.35 
AMS Member Price:  $107.20 $81.20 
with an appendix by Bernard Teissier
Translated by Ben Lichtin
Softcover ISBN:  9780821829837 
Product Code:  ULECT/39 
List Price:  $69.00 
MAA Member Price:  $62.10 
AMS Member Price:  $55.20 
eBook ISBN:  9781470421830 
Product Code:  ULECT/39.E 
List Price:  $65.00 
MAA Member Price:  $58.50 
AMS Member Price:  $52.00 
Softcover ISBN:  9780821829837 
eBook ISBN:  9781470421830 
Product Code:  ULECT/39.B 
List Price:  $134.00 $101.50 
MAA Member Price:  $120.60 $91.35 
AMS Member Price:  $107.20 $81.20 

Book DetailsUniversity Lecture SeriesVolume: 39; 2006; 151 ppMSC: Primary 14
Moduli problems in algebraic geometry date back to Riemann's famous count of the \(3g3\) parameters needed to determine a curve of genus \(g\). In this book, Zariski studies the moduli space of curves of the same equisingularity class. After setting up and reviewing the basic material, Zariski devotes one chapter to the topology of the moduli space, including an explicit determination of the rare cases when the space is compact. Chapter V looks at specific examples where the dimension of the generic component can be determined through rather concrete methods. Zariski's last chapter concerns the application of deformation theory to the moduli problem, including the determination of the dimension of the generic component for a particular family of curves.
An appendix by Bernard Teissier reconsiders the moduli problem from the point of view of deformation theory. He gives new proofs of some of Zariski's results, as well as a natural construction of a compactification of the moduli space.
ReadershipGraduate students and research mathematicians interested in algebraic geometry, especially moduli questions, and singularities.

Table of Contents

Chapters

Chapter 1. Preliminaries

Chapter 2. Equisingularity invariants

Chapter 3. Parametrizations

Chapter 4. The moduli space

Chapter 5. Examples

Chapter 6. Applications of deformation theory

Appendix by B. Teissier

Introduction

Chapter I. The monomial curve $C^\Gamma $ and its formations

Chapter II. Application to the study of the moduli space of a branch

Addendum


Additional Material

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Moduli problems in algebraic geometry date back to Riemann's famous count of the \(3g3\) parameters needed to determine a curve of genus \(g\). In this book, Zariski studies the moduli space of curves of the same equisingularity class. After setting up and reviewing the basic material, Zariski devotes one chapter to the topology of the moduli space, including an explicit determination of the rare cases when the space is compact. Chapter V looks at specific examples where the dimension of the generic component can be determined through rather concrete methods. Zariski's last chapter concerns the application of deformation theory to the moduli problem, including the determination of the dimension of the generic component for a particular family of curves.
An appendix by Bernard Teissier reconsiders the moduli problem from the point of view of deformation theory. He gives new proofs of some of Zariski's results, as well as a natural construction of a compactification of the moduli space.
Graduate students and research mathematicians interested in algebraic geometry, especially moduli questions, and singularities.

Chapters

Chapter 1. Preliminaries

Chapter 2. Equisingularity invariants

Chapter 3. Parametrizations

Chapter 4. The moduli space

Chapter 5. Examples

Chapter 6. Applications of deformation theory

Appendix by B. Teissier

Introduction

Chapter I. The monomial curve $C^\Gamma $ and its formations

Chapter II. Application to the study of the moduli space of a branch

Addendum