Hilbert Functions of Filtered Modules: 9 (Lecture Notes of the Unione Matematica Italiana) - Softcover

Rossi, Maria Evelina Evelina; Valla, Giuseppe

Softcover

ISBN 10: 3642142397 ISBN 13: 9783642142390

Verlag: Springer, 2010

Inhaltsangabe

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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Críticas

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)

Reseña del editor

Starting 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.

Details zur Ausgabe

• Verlag: Springer
• Erscheinungsdatum: 2010
• ISBN 10: 3642142397
• ISBN 13: 9783642142390
• Einband: Tapa blanda
• Sprache: Englisch
• Anzahl der Seiten: 120