Get 40% off of select print and eBooks in Engineering & Materials Science!

Springer Monographs in Mathematics
cover

Integral Closure

Rees Algebras, Multiplicities, Algorithms

Authors: Vasconcelos, Wolmer

Buy this book

eBook $129.00
price for USA in USD (gross)
  • ISBN 978-3-540-26503-0
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $169.99
price for USA in USD
  • ISBN 978-3-540-25540-6
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Softcover $169.99
price for USA in USD
  • ISBN 978-3-642-06492-0
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
About this book

Integral Closure gives an account of theoretical and algorithmic developments on the integral closure of algebraic structures. These are shared concerns in commutative algebra, algebraic geometry, number theory and the computational aspects of these fields. The overall goal is to determine and analyze the equations of the assemblages of the set of solutions that arise under various processes and algorithms. It gives a comprehensive treatment of Rees algebras and multiplicity theory - while pointing to applications in many other problem areas. Its main goal is to provide complexity estimates by tracking numerically invariants of the structures that may occur.

This book is intended for graduate students and researchers in the fields mentioned above. It contains, besides exercises aimed at giving insights, numerous research problems motivated by the developments reported.

About the authors

Author's homepage: http://www.math.rutgers.edu/~vasconce/

Vasconcelos is a well-known top expert in commutative algebra. Author of Algorithms and Computation in Mathematics 2. ISBN: 3-540-21311-2.

Via the existence of the ACM series he was won as a Springer author in 1995, being a CUP author before.

This new book is a result of the good collaboration with him on ACM 2.

Reviews

From the reviews:

"Wolmer Vasconocelos is an authoritative figure in commutative algebra today. … The book under review is an important undertaking and will likely represent an essential research tool for generations to come as well as a standard reference text. … The book is a tour de force in commutative algebra … . Wolmer Vasconcelos does a wonderful job presenting the big picture surrounding the concepts … . This book is recommended to graduate students and mathematicians … . It represents a great addition to the literature." (Florian Enescu, Zentralblatt MATH, Vol. 1082, 2006)

"Integral Closure gives an account of theoretical and algorithmic developments on the integral closure of algebraic structures. … It gives a comprehensive treatment of Rees algebra and multiplicity theory – while pointing to applications in many other problem areas. … This book is intended for graduate students and researchers in the fields mentioned above. It contains, besides exercises aimed at giving insights, numerous research problems motivated by the developments reported." (L’Enseignement Mathematique, Vol. 51 (3-4), 2005)

"The aim of this book is to provide a systematic account of several recent developments on integral closures of ideals and modules in many guises. … This book is addressed to readers who are familiar with basic concepts of commutative algebra, and it could be used for an advanced course … . Graduate students and researchers will find this book useful as a standard reference text on blowup algebras. It contains, besides exercises aimed at giving insights, numerous research problems motivated by recent developments." (Ngô Viêt Trung, Mathematical Reviews, Issue 2006 m)


Table of contents (10 chapters)

Table of contents (10 chapters)
  • Introduction

    Pages 1-16

  • Numerical Invariants of a Rees Algebra

    Pages 17-95

  • Hilbert Functions and Multiplicities

    Pages 97-203

  • Depth and Cohomology of Rees Algebras

    Pages 205-236

  • Divisors of a Rees Algebra

    Pages 237-270

Buy this book

eBook $129.00
price for USA in USD (gross)
  • ISBN 978-3-540-26503-0
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $169.99
price for USA in USD
  • ISBN 978-3-540-25540-6
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Softcover $169.99
price for USA in USD
  • ISBN 978-3-642-06492-0
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Loading...

Recommended for you

Loading...

Bibliographic Information

Bibliographic Information
Book Title
Integral Closure
Book Subtitle
Rees Algebras, Multiplicities, Algorithms
Authors
Series Title
Springer Monographs in Mathematics
Copyright
2005
Publisher
Springer-Verlag Berlin Heidelberg
Copyright Holder
Springer-Verlag Berlin Heidelberg
eBook ISBN
978-3-540-26503-0
DOI
10.1007/b137713
Hardcover ISBN
978-3-540-25540-6
Softcover ISBN
978-3-642-06492-0
Series ISSN
1439-7382
Edition Number
1
Number of Pages
XII, 520
Topics