Progress in Commutative Algebra 1: Combinatorics and Homology

Open Access Published by De Gruyter 2012

Progress in Commutative Algebra 1

Combinatorics and Homology

Edited by: Christopher Francisco , Lee C. Klingler , Sean Sather-Wagstaff and Janet C. Vassilev
With contributions by: Timothy B. P. Clark , Susan M. Cooper , Gunnar Fløystad , Anthony V. Geramita , Brian Harbourne , Livia Hummel , Graham J. Leuschke , Jeff Mermin , Juan C. Migliore , Susan Morey , Paul C. Roberts , Rafael Heraclio Villarreal Rodríguez and Yongwei Yao

In the series De Gruyter Proceedings in Mathematics

https://doi.org/10.1515/9783110250404

Overview
Contents

About this book

This is the first of two volumes of a state-of-the-art survey article collection which originates from three commutative algebra sessions at the 2009 Fall Southeastern American Mathematical Society Meeting at Florida Atlantic University. The articles reach into diverse areas of commutative algebra and build a bridge between Noetherian and non-Noetherian commutative algebra. These volumes present current trends in two of the most active areas of commutative algebra: non-noetherian rings (factorization, ideal theory, integrality), and noetherian rings (the local theory, graded situation, and interactions with combinatorics and geometry).

This volume contains combinatorial and homological surveys. The combinatorial papers document some of the increasing focus in commutative algebra recently on the interaction between algebra and combinatorics. Specifically, one can use combinatorial techniques to investigate resolutions and other algebraic structures as with the papers of Fløystad on Boij-Söderburg theory, of Geramita, Harbourne and Migliore, and of Cooper on Hilbert functions, of Clark on minimal poset resolutions and of Mermin on simplicial resolutions. One can also utilize algebraic invariants to understand combinatorial structures like graphs, hypergraphs, and simplicial complexes such as in the paper of Morey and Villarreal on edge ideals.

Homological techniques have become indispensable tools for the study of noetherian rings. These ideas have yielded amazing levels of interaction with other fields like algebraic topology (via differential graded techniques as well as the foundations of homological algebra), analysis (via the study of D-modules), and combinatorics (as described in the previous paragraph). The homological articles the editors have included in this volume relate mostly to how homological techniques help us better understand rings and singularities both noetherian and non-noetherian such as in the papers by Roberts, Yao, Hummel and Leuschke.

Author / Editor information

Christopher Francisco, Oklahoma State University, Stillwater, Oklahoma, USA; Lee C. Klingler, Florida Atlantic University, Boca Raton, Florida, USA; Sean M. Sather-Wagstaff, North Dakota State University, Fargo, North Dakota, USA; Janet Vassilev, University of New Mexico, Albuquerque, New Mexico, USA.

Supplementary Materials

Inhaltsverzeichnis

Topics

Frontmatter Open Access Download PDF	i
Preface Open Access Download PDF	v
Table of Contents Open Access Download PDF	vii
Boij–Söderberg Theory: Introduction and Survey Gunnar Fløystad Open Access Download PDF	1
Hilbert Functions of Fat Point Subschemes of the Plane: the Two-fold Way Anthony V. Geramita, Brian Harbourne and Juan C. Migliore Open Access Download PDF	55
Edge Ideals: Algebraic and Combinatorial Properties Susan Morey and Rafael H. Villarreal Open Access Download PDF	85
Three Simplicial Resolutions Jeff Mermin Open Access Download PDF	127
A Minimal Poset Resolution of Stable Ideals Timothy B. P. Clark Open Access Download PDF	143
Subsets of Complete Intersections and the EGH Conjecture Susan M. Cooper Open Access Download PDF	167
The Homological Conjectures Paul C. Roberts Open Access Download PDF	199
The Compatibility, Independence, and Linear Growth Properties Yongwei Yao Open Access Download PDF	231
Recent Progress in Coherent Rings: a Homological Perspective Livia Hummel Open Access Download PDF	271
Non-commutative Crepant Resolutions: Scenes From Categorical Geometry Graham J. Leuschke Open Access Download PDF	293

(Deutsch)

Language: English
Publisher: De Gruyter
Audience: Graduate and PhD Students, Researchers, Lecturers; Academic Libraries
Pages
- Front matter: 11
- Main content: 361
Keywords: Commutative Algebra; Combinatirics; Homology

eBook

Published: April 26, 2012
ISBN: 9783110250404

Hardcover

Published: April 16, 2012
ISBN: 9783110250343