Progress in commutative algebra. 1, Combinatorics and homology / edited by Christopher Francisco, Lee Klingler, Sean Sather-Wagstaff, [and] Janet C. Vassilev.

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text

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computer

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online resource

ISBN:

9783110250404
3110250403
9783112190203
3112190203
9783110250343
3110250349
1280570326
9781280570322
9786613599926
6613599921

Other title:

Combinatorics and homology

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Additional physical formats: Print version:: Progress in commutative algebra 1, combinatorics and homology.DDC classification:

512 23

LOC classification:

QA251.3 .P76 2012eb

Online resources:

EBSCOhost

Contents:

Boij-Söderberg theory : introduction and survey / Gunnar Fløystad -- Hilbert functions of fat point subschemes of the plane : the two-fold way / Anthony V. Geramita, Brian Harbourne and Juan C. Migliore -- Edge ideals : algebraic and combinatorial properties / Susan Morey and Rafael H. Villarreal -- Three simplicial resolutions / Jeff Mermin -- A minimal poset resolution of stable ideals / Timothy B.P. Clark -- Subsets of complete intersections and the EGH conjecture / Susan M. Cooper -- The homological conjectures / Paul C. Roberts -- The compatibility, independence, and linear growth properties / Yongwei Yao -- Recent progress in coherent rings : a homological perspective / Livia Hummel -- Non-commutative crepant resolutions : scenes from categorical geometry / Graham J. Leuschke.

Summary: 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. 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. The homological articles in this volume relate mostly to how homological techniques help us better understand rings and singularities both noetherian and non-noetherian.

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Includes bibliographical references at chapter ends.

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. 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. The homological articles in this volume relate mostly to how homological techniques help us better understand rings and singularities both noetherian and non-noetherian.