Hilbert Functions of Filtered Modules [electronic resource] /
Rossi, Maria Evelina.author.
Valla, Giuseppe.author.
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.
Description based upon print version of record.
Hilbert Functions of Filtered Modules; Preface; Acknowledgements; Contents; Introduction; Chapter 1 Preliminaries; Chapter 2 Bounds for e0(M) and e1(M); Chapter 3 Bounds for e2(M); Chapter 4 Sally's Conjecture and Applications; Chapter 5 Applications to the Fiber Cone; Chapter 6 Applications to the Sally Module; References; Index
Includes bibliographical references and index.
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.
Algebra.
Commutative algebra.
Commutative rings.
Algebraic geometry.
Algebra.
Commutative Rings and Algebras.
Algebraic Geometry.
Lecture Notes of the Unione Matematica Italiana