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Analytic and Algebraic Geometry: Common Problems, Different Methods
 
Edited by: Jeffery McNeal Ohio State University, Columbus, OH
Mircea Mustaţă University of Michigan, Ann Arbor, MI
A co-publication of the AMS and IAS/Park City Mathematics Institute
Analytic and Algebraic Geometry
Hardcover ISBN:  978-0-8218-4908-8
Product Code:  PCMS/17
List Price: $125.00
MAA Member Price: $112.50
AMS Member Price: $100.00
eBook ISBN:  978-1-4704-1631-7
Product Code:  PCMS/17.E
List Price: $112.00
MAA Member Price: $100.80
AMS Member Price: $89.60
Hardcover ISBN:  978-0-8218-4908-8
eBook: ISBN:  978-1-4704-1631-7
Product Code:  PCMS/17.B
List Price: $237.00 $181.00
MAA Member Price: $213.30 $162.90
AMS Member Price: $189.60 $144.80
Analytic and Algebraic Geometry
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Analytic and Algebraic Geometry: Common Problems, Different Methods
Edited by: Jeffery McNeal Ohio State University, Columbus, OH
Mircea Mustaţă University of Michigan, Ann Arbor, MI
A co-publication of the AMS and IAS/Park City Mathematics Institute
Hardcover ISBN:  978-0-8218-4908-8
Product Code:  PCMS/17
List Price: $125.00
MAA Member Price: $112.50
AMS Member Price: $100.00
eBook ISBN:  978-1-4704-1631-7
Product Code:  PCMS/17.E
List Price: $112.00
MAA Member Price: $100.80
AMS Member Price: $89.60
Hardcover ISBN:  978-0-8218-4908-8
eBook ISBN:  978-1-4704-1631-7
Product Code:  PCMS/17.B
List Price: $237.00 $181.00
MAA Member Price: $213.30 $162.90
AMS Member Price: $189.60 $144.80
  • Book Details
     
     
    IAS/Park City Mathematics Series
    Volume: 172010; 583 pp
    MSC: Primary 14; 32; 53;

    Analytic and algebraic geometers often study the same geometric structures but bring different methods to bear on them. While this dual approach has been spectacularly successful at solving problems, the language differences between algebra and analysis also represent a difficulty for students and researchers in geometry, particularly complex geometry.

    The PCMI program was designed to partially address this language gulf, by presenting some of the active developments in algebraic and analytic geometry in a form suitable for students on the “other side” of the analysis-algebra language divide. One focal point of the summer school was multiplier ideals, a subject of wide current interest in both subjects.

    The present volume is based on a series of lectures at the PCMI summer school on analytic and algebraic geometry. The series is designed to give a high-level introduction to the advanced techniques behind some recent developments in algebraic and analytic geometry. The lectures contain many illustrative examples, detailed computations, and new perspectives on the topics presented, in order to enhance access of this material to non-specialists.

    Titles in this series are co-published with the Institute for Advanced Study/Park City Mathematics Institute.

    Readership

    Graduate students and research mathematicians interested in modern algebraic geometry and modern complex analytic geometry.

  • Table of Contents
     
     
    • Chapters
    • Introduction
    • An introduction to things $\overline {\partial }$
    • Real and complex geometry meet the Cauchy-Riemann equations
    • Three variations on a theme in complex analytic geometry
    • Structure theorems for projective and Kähler varieties
    • Lecture notes on rational polytopes and finite generation
    • Introduction to resolution of singularities
    • A short course on multiplier ideals
    • Exercises in the birational geometry of algebraic varieties
    • Higher dimensional minimal model program for varieties of log general type
    • Lectures on flips and minimal models
  • Additional Material
     
     
  • Reviews
     
     
    • This book succeeds [in] making explicit the bridges between the algebraic and analytic approaches, closing the language differences and at the same time introducing graduate students and researchers to a major development in complex algebraic geometry.

      MAA Reviews
  • Requests
     
     
    Review Copy – for publishers of book reviews
    Accessibility – to request an alternate format of an AMS title
Volume: 172010; 583 pp
MSC: Primary 14; 32; 53;

Analytic and algebraic geometers often study the same geometric structures but bring different methods to bear on them. While this dual approach has been spectacularly successful at solving problems, the language differences between algebra and analysis also represent a difficulty for students and researchers in geometry, particularly complex geometry.

The PCMI program was designed to partially address this language gulf, by presenting some of the active developments in algebraic and analytic geometry in a form suitable for students on the “other side” of the analysis-algebra language divide. One focal point of the summer school was multiplier ideals, a subject of wide current interest in both subjects.

The present volume is based on a series of lectures at the PCMI summer school on analytic and algebraic geometry. The series is designed to give a high-level introduction to the advanced techniques behind some recent developments in algebraic and analytic geometry. The lectures contain many illustrative examples, detailed computations, and new perspectives on the topics presented, in order to enhance access of this material to non-specialists.

Titles in this series are co-published with the Institute for Advanced Study/Park City Mathematics Institute.

Readership

Graduate students and research mathematicians interested in modern algebraic geometry and modern complex analytic geometry.

  • Chapters
  • Introduction
  • An introduction to things $\overline {\partial }$
  • Real and complex geometry meet the Cauchy-Riemann equations
  • Three variations on a theme in complex analytic geometry
  • Structure theorems for projective and Kähler varieties
  • Lecture notes on rational polytopes and finite generation
  • Introduction to resolution of singularities
  • A short course on multiplier ideals
  • Exercises in the birational geometry of algebraic varieties
  • Higher dimensional minimal model program for varieties of log general type
  • Lectures on flips and minimal models
  • This book succeeds [in] making explicit the bridges between the algebraic and analytic approaches, closing the language differences and at the same time introducing graduate students and researchers to a major development in complex algebraic geometry.

    MAA Reviews
Review Copy – for publishers of book reviews
Accessibility – to request an alternate format of an AMS title
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