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The Moduli Problem for Plane Branches

with an appendix by Bernard Teissier

Translated by Ben Lichtin
Available Formats:
Softcover ISBN: 978-0-8218-2983-7
Product Code: ULECT/39
List Price: $41.00 MAA Member Price:$36.90
AMS Member Price: $32.80 Electronic ISBN: 978-1-4704-2183-0 Product Code: ULECT/39.E List Price:$38.00
MAA Member Price: $34.20 AMS Member Price:$30.40
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List Price: $61.50 MAA Member Price:$55.35
AMS Member Price: $49.20 Click above image for expanded view The Moduli Problem for Plane Branches with an appendix by Bernard Teissier Translated by Ben Lichtin Available Formats:  Softcover ISBN: 978-0-8218-2983-7 Product Code: ULECT/39  List Price:$41.00 MAA Member Price: $36.90 AMS Member Price:$32.80
 Electronic ISBN: 978-1-4704-2183-0 Product Code: ULECT/39.E
 List Price: $38.00 MAA Member Price:$34.20 AMS Member Price: $30.40 Bundle Print and Electronic Formats and Save! This product is available for purchase as a bundle. Purchasing as a bundle enables you to save on the electronic version.  List Price:$61.50 MAA Member Price: $55.35 AMS Member Price:$49.20
• Book Details

University Lecture Series
Volume: 392006; 151 pp
MSC: Primary 14;

Moduli problems in algebraic geometry date back to Riemann's famous count of the $3g-3$ 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

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Volume: 392006; 151 pp
MSC: Primary 14;

Moduli problems in algebraic geometry date back to Riemann's famous count of the $3g-3$ 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