Hilbert functions of filtered modules

✍ Scribed by Giuseppe Valla, Maria Evelina Rossi (auth.)

• Publisher: Springer-Verlag Berlin Heidelberg
• Year: 2010
• Tongue: English
• Leaves: 120
• Series: Lecture Notes of the Unione Matematica Italiana 9
• Edition: 1
• Category: Library

✦ Synopsis

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.

✦ Table of Contents

Front Matter....Pages i-xviii
Preliminaries....Pages 1-14
Bounds for $${e}{0}(\mathbb{M})$$ and $${e}{1}(\mathbb{M})$$ ....Pages 15-46
Bounds for $${e}_{2}(\mathbb{M})$$ ....Pages 47-59
Sally’s Conjecture and Applications....Pages 61-76
Applications to the Fiber Cone....Pages 77-86
Applications to the Sally Module....Pages 87-91
Back Matter....Pages 93-101

✦ Subjects

Algebra; Commutative Rings and Algebras; Algebraic Geometry