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Lecture Notes of the Unione Matematica Italiana

Ideals of Powers and Powers of Ideals

Intersecting Algebra, Geometry, and Combinatorics

Authors: Carlini, E., , H.T., Harbourne, B., Van Tuyl, A.

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  • First book to contain a summary of known results on the associated primes of edge ideals
  • First book to contain a summary of known results on the regularity of powers of monomial ideals
  • Contains open problems for graduate students 
  • With a chapter for early career researchers on "how to do mathematics research" 
  • Provides an up-to-date and comprehensive list of references of papers in the area
  • Written by authors who have made numerous contributions to these areas
  • First book to introduce the ideal containment problem (e.g. Waldschmidt contstant resurgence symbolic defect)
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eBook $29.99
$59.99 (listprice)
price for USA in USD
valid through June 30, 2021
  • ISBN 978-3-030-45247-6
  • Digitally watermarked, DRM-free
  • Included format: PDF, EPUB
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Softcover $39.99
$79.99 (listprice)
price for USA in USD
valid through June 30, 2021
  • ISBN 978-3-030-45246-9
  • Free shipping for individuals worldwide
  • Institutional customers should get in touch with their account manager
  • Covid-19 shipping restrictions
  • Usually ready to be dispatched within 3 to 5 business days, if in stock
About this book

This book discusses regular powers and symbolic powers of ideals from three perspectives– algebra, combinatorics and geometry – and examines the interactions between them. It invites readers to explore the evolution of the set of associated primes of higher and higher powers of an ideal and explains the evolution of ideals associated with combinatorial objects like graphs or hypergraphs in terms of the original combinatorial objects. It also addresses similar questions concerning  our understanding of the Castelnuovo-Mumford regularity of powers of combinatorially defined ideals in terms of the associated combinatorial data. From a more geometric point of view, the book considers how the relations between symbolic and regular powers can be interpreted in geometrical terms.  Other topics covered include aspects of Waring type problems, symbolic powers of an ideal and their invariants (e.g., the Waldschmidt constant, the resurgence), and the persistence of associated primes.

Reviews

“This is a very interesting monograph providing a fast introduction to different fields of research devoted to modern aspects and develompents of commutative algebra, algebraic geometry, combinatorics, etc.” (Piotr Pokora, zbMATH 1445.13001, 2020)


Table of contents (20 chapters)

Table of contents (20 chapters)

Buy this book

eBook $29.99
$59.99 (listprice)
price for USA in USD
valid through June 30, 2021
  • ISBN 978-3-030-45247-6
  • Digitally watermarked, DRM-free
  • Included format: PDF, EPUB
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Softcover $39.99
$79.99 (listprice)
price for USA in USD
valid through June 30, 2021
  • ISBN 978-3-030-45246-9
  • Free shipping for individuals worldwide
  • Institutional customers should get in touch with their account manager
  • Covid-19 shipping restrictions
  • Usually ready to be dispatched within 3 to 5 business days, if in stock
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Bibliographic Information

Bibliographic Information
Book Title
Ideals of Powers and Powers of Ideals
Book Subtitle
Intersecting Algebra, Geometry, and Combinatorics
Authors
Series Title
Lecture Notes of the Unione Matematica Italiana
Series Volume
27
Copyright
2020
Publisher
Springer International Publishing
Copyright Holder
The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG
eBook ISBN
978-3-030-45247-6
DOI
10.1007/978-3-030-45247-6
Softcover ISBN
978-3-030-45246-9
Series ISSN
1862-9113
Edition Number
1
Number of Pages
XIX, 161
Number of Illustrations
21 b/w illustrations
Topics