Overview
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.
Full Product Details
Author: Maria Evelina Rossi ,
Giuseppe Valla
Publisher: Springer-Verlag Berlin and Heidelberg GmbH & Co. KG
Imprint: Springer-Verlag Berlin and Heidelberg GmbH & Co. K
Edition: 2010 ed.
Volume: 9
Dimensions:
Width: 15.50cm
, Height: 0.60cm
, Length: 23.50cm
Weight: 0.454kg
ISBN: 9783642142390
ISBN 10: 3642142397
Pages: 100
Publication Date: 18 September 2010
Audience:
Professional and scholarly
,
Professional & Vocational
Format: Paperback
Publisher's Status: Active
Availability: In Print
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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. (Le Tua n 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)
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. (Le Tua n Hoa, Mathematical Reviews, Issue 2012 b)
