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Hilbert Functions of Filtered Modules: Lecture Notes of the Unione Matematica Italiana, cartea 9

Autor Maria Evelina Rossi, Giuseppe Valla
en Limba Engleză Paperback – 18 sep 2010
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.
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Specificații

ISBN-13: 9783642142390
ISBN-10: 3642142397
Pagini: 120
Ilustrații: XVIII, 100 p.
Dimensiuni: 155 x 235 x 10 mm
Greutate: 0.18 kg
Ediția:2010
Editura: Springer Berlin, Heidelberg
Colecția Springer
Seria Lecture Notes of the Unione Matematica Italiana

Locul publicării:Berlin, Heidelberg, Germany

Public țintă

Graduate

Cuprins

Preliminaries.- Bounds for and

Recenzii

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)

Textul de pe ultima copertă

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.

Caracteristici

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