Format:
Online-Ressource (1 online resource (xi, 361 p.))
,
ill.
Edition:
Online-Ausg.
ISBN:
9783110250404
,
9783110278606
,
9783112190203
,
9783110278613
,
9781280570322
,
1280569565
,
9781280569562
Series Statement:
De Gruyter proceedings in mathematics
Content:
The series is aimed specifically at publishing peer reviewed reviews and contributions presented at workshops and conferences. Each volume is associated with a particular conference, symposium or workshop. These events cover various topics within pure and applied mathematics and provide up-to-date coverage of new developments, methods and applications.
Content:
Intro -- Preface -- Boij-Söderberg Theory: Introduction and Survey -- 1 The Boij-Söderberg Conjectures -- 1.1 Resolutions and Betti Diagrams -- 1.2 The Positive Cone of Betti Diagrams -- 1.3 Herzog-Kühl Equations -- 1.4 Pure resolutions -- 1.5 Linear Combinations of Pure Diagrams -- 1.6 The Boij-Söderberg Conjectures -- 1.7 Algorithmic Interpretation -- 1.8 Geometric Interpretation -- 2 The Exterior Facets of the Boij-Söderberg Fan and Their Supporting Hyperplanes -- 2.1 The Exterior Facets -- 2.2 The Supporting Hyperplanes -- 2.3 Pairings of Vector Bundles and Resolutions -- 3 The Existence of Pure Free Resolutions and of Vector Bundles with Supernatural Cohomology -- 3.1 The Equivariant Pure Free Resolution -- 3.2 Equivariant Supernatural Bundles -- 3.3 Characteristic Free Supernatural Bundles -- 3.4 The Characteristic Free Pure Resolutions -- 3.5 Pure Resolutions Constructed from Generic Matrices -- 4 Cohomology of Vector Bundles on Projective Spaces -- 4.1 Cohomology Tables -- 4.2 The Fan of Cohomology Tables of Vector Bundles -- 4.3 Facet Equations -- 5 Extensions to Non-Cohen-Macaulay Modules and to Coherent Sheaves -- 5.1 Betti Diagrams of Graded Modules in General -- 5.2 Cohomology of Coherent Sheaves -- 6 Further Topics -- 6.1 The Semigroup of Betti Diagrams of Modules -- 6.2 Variations on the Grading -- 6.3 Poset Structures -- 6.4 Computer Packages -- 6.5 Three Basic Problems -- Hilbert Functions of Fat Point Subschemes of the Plane: the Two-fold Way -- 1 Introduction -- 2 Approach I: Nine Double Points -- 3 Approach I: Points on Cubics -- 4 Approach II: Points on Cubics -- Edge Ideals: Algebraic and Combinatorial Properties -- 1 Introduction -- 2 Algebraic and Combinatorial Properties of Edge Ideals -- 3 Invariants of Edge Ideals: Regularity, Projective Dimension, Depth -- 4 Stability of Associated Primes.
Note:
Includes bibliographical references and index. - Description based on print version record
Additional Edition:
ISBN 9783110250343
Additional Edition:
ISBN 9783110278590
Additional Edition:
ISBN 9783112190203
Additional Edition:
ISBN 9783110278613
Additional Edition:
ISBN 1280569344
Additional Edition:
ISBN 9783110250404
Additional Edition:
ISBN 1280570164
Additional Edition:
ISBN 9783110278606
Additional Edition:
Erscheint auch als Druck-Ausgabe Progress in commutative algebra ; 1: Combinatorics and homology Berlin [u.a.] : De Gruyter, 2012 ISBN 9783110250343
Language:
German
URL:
Volltext
(lizenzpflichtig)
URL:
Volltext
(lizenzpflichtig)
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