Progress in commutative algebra. 1, Combinatorics and homology /
Progress in commutative algebra. 1, Combinatorics and homology /
Combinatorics and homology
edited by Christopher Francisco, Lee Klingler, Sean Sather-Wagstaff, [and] Janet C. Vassilev.
- 1 online resource (xii, 364 pages) : illustrations
- De Gruyter Proceedings in Mathematics .
- Gruyter Proceedings in Mathematics. .
Includes bibliographical references at chapter ends.
Boij-Söderberg theory : introduction and survey / Hilbert functions of fat point subschemes of the plane : the two-fold way / Edge ideals : algebraic and combinatorial properties / Three simplicial resolutions / A minimal poset resolution of stable ideals / Subsets of complete intersections and the EGH conjecture / The homological conjectures / The compatibility, independence, and linear growth properties / Recent progress in coherent rings : a homological perspective / Non-commutative crepant resolutions : scenes from categorical geometry / Gunnar Fløystad -- Anthony V. Geramita, Brian Harbourne and Juan C. Migliore -- Susan Morey and Rafael H. Villarreal -- Jeff Mermin -- Timothy B.P. Clark -- Susan M. Cooper -- Paul C. Roberts -- Yongwei Yao -- Livia Hummel -- Graham J. Leuschke.
Open Access
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.
In English.
9783110250404 3110250403 9783112190203 3112190203 9783110250343 3110250349 1280570326 9781280570322 9786613599926 6613599921
10.1515/9783110250404 doi
102374 Knowledge Unlatched
Commutative algebra.
Algebra.
MATHEMATICS--Algebra--Intermediate.
Commutative algebra.
Electronic books.
Electronic books.
QA251.3 / .P76 2012eb
512
Includes bibliographical references at chapter ends.
Boij-Söderberg theory : introduction and survey / Hilbert functions of fat point subschemes of the plane : the two-fold way / Edge ideals : algebraic and combinatorial properties / Three simplicial resolutions / A minimal poset resolution of stable ideals / Subsets of complete intersections and the EGH conjecture / The homological conjectures / The compatibility, independence, and linear growth properties / Recent progress in coherent rings : a homological perspective / Non-commutative crepant resolutions : scenes from categorical geometry / Gunnar Fløystad -- Anthony V. Geramita, Brian Harbourne and Juan C. Migliore -- Susan Morey and Rafael H. Villarreal -- Jeff Mermin -- Timothy B.P. Clark -- Susan M. Cooper -- Paul C. Roberts -- Yongwei Yao -- Livia Hummel -- Graham J. Leuschke.
Open Access
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.
In English.
9783110250404 3110250403 9783112190203 3112190203 9783110250343 3110250349 1280570326 9781280570322 9786613599926 6613599921
10.1515/9783110250404 doi
102374 Knowledge Unlatched
Commutative algebra.
Algebra.
MATHEMATICS--Algebra--Intermediate.
Commutative algebra.
Electronic books.
Electronic books.
QA251.3 / .P76 2012eb
512