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Title Configuration spaces : geometry, topology and representation theory / Filippo Callegaro, Frederick Cohen, Corrado De Concini, Eva Maria Feichtner, Giovanni Gaiffi, Mario Salvetti, editors.

Published Switzerland : Springer, [2016]


Location Call No. Status
Physical description 1 online resource.
Series Springer INdAM series ; Volume 14
Springer INdAM series ; Volume 14.
Springer English/International eBooks 2016 - Full Set
Springer Mathematics and Statistics eBooks 2016 English+International
Bibliography Includes bibliographical references.
Contents Preface; Contents; Contributors; About the Editors; Around the Tangent Cone Theorem; 1 Introduction; 1.1 Resonance Varieties; 1.2 Characteristic Varieties; 1.3 Quasi-Projective Varieties; 2 The Resonance Varieties of a cdga; 2.1 Commutative Differential Graded Algebras; 2.2 Resonance Varieties; 2.3 A Generalized Koszul Complex; 2.4 Alternate Views of Resonance; 3 The Resonance Varieties of a Space; 3.1 The Cohomology Algebra; 3.2 The Sullivan Model; 3.3 An Algebraic Tangent Cone Theorem; 3.4 Positive Weights; 4 Characteristic Varieties; 4.1 Homology Jump Loci for Rank 1 Local Systems
4.2 Some Properties of the Characteristic Varieties4.3 Alexander Varieties; 5 The Tangent Cone Theorem; 5.1 Two Types of Tangent Cones; 5.2 Germs of Jump Loci; 5.3 Tangent Cones and Jump Loci; 5.4 The Influence of Formality; 5.5 Formality Tests; 6 Smooth Quasi-Projective Varieties; 6.1 Compactifications and Formality; 6.2 Algebraic Models; 6.3 Configuration Spaces; 6.4 Characteristic Varieties; 6.5 Resonance Varieties; 6.6 Resonance in Degree 1; 7 Hyperplane Arrangements and the Milnor Fibration; 7.1 Complement and Intersection Lattice; 7.2 Cohomology Jump Loci of the Complement
7.3 The Milnor Fibration7.4 Cohomology Jump Loci of the Milnor Fiber; 7.5 Formality of the Milnor Fiber; 8 Elliptic Arrangements; 8.1 Complements of Elliptic Arrangements; 8.2 An Algebraic Model; 8.3 Ordered Configurations on an Elliptic Curve; References; Higher Resonance Varieties of Matroids; 1 Introduction; 1.1 Outline; 2 Background; 2.1 Arrangements and Matroids; 2.2 Projectivization; 2.3 A Category of Matroids; 3 Resonance Varieties; 3.1 Definitions; 3.2 Resonance of Orlik-Solomon Algebras; 3.3 Top and Bottom; 3.4 Upper Bounds; 4 Matroid Operations and Resonance; 4.1 Naturality
4.2 Sums, Submatroids and Duals4.3 Local Components; 4.4 Deletion-Contraction; 4.5 Parallel Connections; 5 Singular Subspaces and Multinets; 5.1 R1(M): Multinets; 5.2 R≥1(M): Singular Subspaces; References; Local Asymptotic Euler-Maclaurin Expansion for Riemann Sums over a Semi-Rational Polyhedron; 1 Introduction; 2 Notations and Basic Facts; 2.1 Various Notations; 2.1.1 Vector Spaces; 2.1.2 Bernoulli Numbers and Polynomials; 2.1.3 Fractional Part of a Real Number; 2.1.4 Fourier Transform; 2.2 Polyhedra, Cones; 2.2.1 Convex Polyhedron; 2.2.2 Subdivision of a Cone into Unimodular Ones
2.3 Discrete and Continuous Generating Functions of a Pointed Polyhedron S(p), I(p)3 Asymptotic Expansions for Riemann Sums over a Cone ; 3.1 Dimension One; 3.2 Fourier Transforms and Boundary Values; 3.3 Asymptotic Expansion of the Fourier Transform of a Riemann Sum over a Cone; 3.4 Asymptotic Expansions of Riemann Sums over Cones in Terms of Differential Operators; 4 Simplicial Cones and Normal Derivatives Formula; 4.1 Asymptotic Expansions of Riemann Sums and Todd Operator; 4.2 Local Euler-Maclaurin Formula
Other author Callegaro, Filippo, editor.
Cohen, Frederick, editor.
De Concini, Corrado, editor.
Feichtner, Eva Maria, editor.
Gaiffi, Giovanni, editor.
Salvetti, Mario, editor.
SpringerLink issuing body.
Subject Topology.
Electronic books.
ISBN 9783319315805 (electronic bk.)
3319315803 (electronic bk.)