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Hilbert Functions of Filtered Modules

  • Book
  • © 2010

Overview

Authors:
  1. Giuseppe Valla

    1. , Department of Mathematics, University of Genoa, Genova, Italy

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  2. Maria Evelina Rossi

    1. Department of Mathematics, University of Genoa, Genoa, Italy

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    You can also search for this author in PubMed   Google Scholar

  • There are not similar books on the topic
  • Hilbert functions are becoming of increasing interest
  • Numerous examples help the reader
  • It includes new developments and easier proofs of classical results
  • Includes supplementary material: sn.pub/extras

Part of the book series: Lecture Notes of the Unione Matematica Italiana (UMILN, volume 9)

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Table of contents (6 chapters)

  1. Front Matter

    Pages i-xviii
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  2. Preliminaries

    • Maria Evelina Rossi, Giuseppe Valla
    Pages 1-14

  3. Bounds for \({e}_{0}(\mathbb{M})\) and \({e}_{1}(\mathbb{M})\)

    • Maria Evelina Rossi, Giuseppe Valla
    Pages 15-46

  4. Bounds for \({e}_{2}(\mathbb{M})\)

    • Maria Evelina Rossi, Giuseppe Valla
    Pages 47-59

  5. Sally’s Conjecture and Applications

    • Maria Evelina Rossi, Giuseppe Valla
    Pages 61-76

  6. Applications to the Fiber Cone

    • Maria Evelina Rossi, Giuseppe Valla
    Pages 77-86

  7. Applications to the Sally Module

    • Maria Evelina Rossi, Giuseppe Valla
    Pages 87-91

  8. Back Matter

    Pages 93-101
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Keywords

About this book

Hilbert Functions play major roles in Algebraic Geometry and Commutative Algebra, and are becoming increasingly important also 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 place many new developments of this theory by using a unifying approach which gives 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 the monograph. The material is intended for graduate students and researchers who are interested in Commutative Algebra, in particular 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)

Authors and Affiliations

  • , Department of Mathematics, University of Genoa, Genova, Italy

    Giuseppe Valla

  • Department of Mathematics, University of Genoa, Genoa, Italy

    Maria Evelina Rossi

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