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Lecture Notes of the Unione Matematica Italiana Ser.: Hilbert Functions of Filtered Modules by Maria Evelina Rossi and Giuseppe Valla (2010, Trade Paperback)
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About this product
Product Identifiers
PublisherSpringer Berlin / Heidelberg
ISBN-103642142397
ISBN-139783642142390
eBay Product ID (ePID)109293041
Product Key Features
Number of PagesXviii, 100 Pages
Publication NameHilbert Functions of Filtered Modules
LanguageEnglish
SubjectAlgebra / Abstract, Functional Analysis, Algebra / General, Geometry / Algebraic
Publication Year2010
TypeTextbook
Subject AreaMathematics
AuthorMaria Evelina Rossi, Giuseppe Valla
SeriesLecture Notes of the Unione Matematica Italiana Ser.
FormatTrade Paperback
Dimensions
Item Weight16 Oz
Item Length9.3 in
Item Width6.1 in
Additional Product Features
Intended AudienceScholarly & Professional
ReviewsFrom 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." (L Tun 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. (Lê Tun Hoa, Mathematical Reviews, Issue 2012 b), 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 Tun 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)
Series Volume Number9
Number of Volumes1 vol.
IllustratedYes
SynopsisStarting from the pioneering work of D.G. Northcott and J. Sally, this volume presents new developments of Hilbert Functions in one cohesive reference. The text applies the theory to the study of certain graded algebras which are not associated to a filtration., 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.
LC Classification NumberQA150-272
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