Lecture Notes of the Unione Matematica Italiana

Hilbert Functions of Filtered Modules

Authors: Rossi, Maria Evelina, Valla, Giuseppe

  • Provides a unique perspective on the topic
  • Covers Hilbert functions -- a topic of increasing interest
  • Presents numerous examples that help readers understand the concepts discussed
  • Includes new developments and easier proofs of classical results
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About this book

Hilbert functions play major parts in Algebraic Geometry and Commutative Algebra, and are also becoming increasingly important in Computational Algebra. They capture many useful numerical characters associated to a projective variety or to a filtered module over a local ring. Starting from the pioneering work of D.G. Northcott and J. Sally, we aim to gather together in one book a broad range of new developments in this theory by using a unifying approach which yields self-contained and easier proofs. The extension of the theory to the case of general filtrations on a module, and its application to the study of certain graded algebras which are not associated to a filtration are two of the main features of this work. The material is intended for graduate students and researchers who are interested in Commutative Algebra, particularly in the theory of the Hilbert functions and related topics.

Reviews

From the reviews:

“This book’s first aim is to gather together in one place many new developments of the theory of Hilbert functions by using a unifying approach of filtrations of submodules. In this way, the book not only extends many well-known results … but it also gives self-contained and easier proofs of even classical results. … This is a short but very nice book. It is useful for graduate students and researchers who are interested in the theory of Hilbert functions.” (Lê Tuấn Hoa, Mathematical Reviews, Issue 2012 b)

“The authors introduce and discuss the notion of a good q-filtration of a module over a local ring. … The authors give several upper bounds for the first two Hilbert coefficients of the Hilbert polynomial of a filtration … . This is an interesting and well written lecture note.” (Siamak Yassemi, Zentralblatt MATH, Vol. 1201, 2011)


Table of contents (6 chapters)

  • Preliminaries

    Rossi, Maria Evelina (et al.)

    Pages 1-14

  • Bounds for $${e}_{0}(\mathbb{M})$$ and $${e}_{1}(\mathbb{M})$$

    Rossi, Maria Evelina (et al.)

    Pages 15-46

  • Bounds for $${e}_{2}(\mathbb{M})$$

    Rossi, Maria Evelina (et al.)

    Pages 47-59

  • Sally’s Conjecture and Applications

    Rossi, Maria Evelina (et al.)

    Pages 61-76

  • Applications to the Fiber Cone

    Rossi, Maria Evelina (et al.)

    Pages 77-86

Buy this book

eBook $34.99
price for USA (gross)
  • ISBN 978-3-642-14240-6
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Softcover $49.95
price for USA
  • ISBN 978-3-642-14239-0
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
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Bibliographic Information

Bibliographic Information
Book Title
Hilbert Functions of Filtered Modules
Authors
Series Title
Lecture Notes of the Unione Matematica Italiana
Series Volume
9
Copyright
2010
Publisher
Springer-Verlag Berlin Heidelberg
Copyright Holder
Springer-Verlag Berlin Heidelberg
eBook ISBN
978-3-642-14240-6
DOI
10.1007/978-3-642-14240-6
Softcover ISBN
978-3-642-14239-0
Series ISSN
1862-9113
Edition Number
1
Number of Pages
XVIII, 100
Topics