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PRINTED BOOKS

Title Moduli spaces / edited by Leticia Brambila-Paz, Oscar García-Prada, Peter Newstead, Richard P. Thomas.

Published Cambridge : Cambridge University Press, 2014.
©2014.

Copies

Location Call No. Status
 UniM ERC  516.35 MODU    AVAILABLE
Physical description xi, 333 pages : illustrations ; 23 cm.
Series London Mathematical Society lecture note series ; 411.
London Mathematical Society lecture note series ; 411.
Bibliography Includes bibliographical references.
Contents 1.Introduction to algebraic stacks / K. Behrend -- Introduction -- 1.1.Topological stacks: triangles -- 1.1.1.Families and their symmetry groupoids -- 1.1.2.Continuous families -- 1.1.3.Classification -- 1.1.4.Scalene triangles -- 1.1.5.Isosceles triangles -- 1.1.6.Equilateral triangles -- 1.1.7.Oriented triangles -- 1.1.8.Stacks -- 1.1.9.Versal families -- 1.1.10.Degenerate triangles -- 1.1.11.Change of versal family -- 1.1.12.Weierstrass compactification -- 1.2.Formalism -- 1.2.1.Objects in continuous families: categories fibered in groupoids -- 1.2.2.Families characterized locally: prestacks -- 1.2.3.Families which can be glued: stacks -- 1.2.4.Topological stacks -- 1.2.5.Deligne-Mumford topological stacks -- 1.2.6.Lattices up to homothety -- 1.2.7.Fundamental groups of topological stacks -- 1.3.Algebraic stacks -- 1.3.1.Groupoid fibrations -- 1.3.2.Prestacks -- 1.3.3.Algebraic stacks -- 1.3.4.The coarse moduli space --
Contents note continued: 1.3.5.Bundles on stacks -- 1.3.6.Stacky curves: the Riemann-Roch theorem -- 2.BPS states and the P = W conjecture / G. Pan -- 2.1.Introduction -- 2.2.Hausel-Rodriguez-Villegas formula and P = W -- 2.2.1.Hausel-Rodriguez-Villegas formula -- 2.2.2.Hitchin system and P = W -- 2.3.Refined stable pair invariants of local curves -- 2.3.1.TQFT formalism -- 2.3.2.Refined invariants from instanton sums -- 2.4.HRV formula as a refined GV expansion -- 3.Representations of surface groups and Higgs bundles / Peter B. Gothen -- 3.1.Introduction -- 3.2.Lecture 1: Character varieties for surface groups and harmonic maps -- 3.2.1.Surface group representations and character varieties -- 3.2.2.Review of connections and curvature in principal bundles -- 3.2.3.Surface group representations and flat bundles -- 3.2.4.Flat bundles and gauge equivalence -- 3.2.5.Harmonic metrics in flat bundles -- 3.2.6.The Corlette--Donaldson theorem --
Contents note continued: 3.3.Lecture 2: G-Higgs bundles and the Hitchin--Kobayashi correspondence -- 3.3.1.Lie theoretic preliminaries -- 3.3.2.The Hitchin equations -- 3.3.3.G-Higgs bundles, stability and the Hitchin-Kobayashi correspondence -- 3.3.4.The Hitchin map -- 3.3.5.The moduli space of SU (p, q)-Higgs bundles -- 3.4.Lecture 3: Morse--Bott theory of the moduli space of G-Higgs bundles -- 3.4.1.Simple and infinitesimally simple G-Higgs bundles -- 3.4.2.Deformation theory of G-Higgs bundles -- 3.4.3.The C*-action and topology of moduli spaces -- 3.4.4.Calculation of Morse indices -- 3.4.5.The moduli space of Sp(2n, R)-Higgs bundles -- 4.Introduction to stability conditions / D. Huybrechts -- 4.1.Torsion theories and t-structures -- 4.1.1.μ-stability on curves (and surfaces): recollections -- 4.1.2.Torsion theories in abelian categories -- 4.1.3.t-structures on triangulated categories -- 4.1.4.Torsion theories versus t-structures --
Contents note continued: 4.2.Stability conditions: definition and examples -- 4.2.1.Slicings -- 4.2.2.Stability conditions -- 4.2.3.Aut(D)-action and GL+(2, R)-action -- 4.2.4.Stability conditions on curves -- 4.3.Stability conditions on surfaces -- 4.3.1.Classification of hearts -- 4.3.2.Construction of hearts -- 4.4.The topological space of stability conditions -- 4.4.1.Topology of Slice(D) -- 4.4.2.Topology of Stab(D) -- 4.4.3.Main result -- 4.5.Stability conditions on K3 surfaces -- 4.5.1.Main theorem and conjecture -- 4.5.2.Autoequivalences -- 4.5.3.Building up Stab(X)° -- 4.5.4.Moduli space rephrasing -- 4.6.Further results -- 4.6.1.Non-compact cases -- 4.6.2.Compact cases -- 5.An introduction to d-manifolds and derived differential geometry / Dominic Joyce -- 5.1.Introduction -- 5.2.C[∞]-rings and C[∞]-schemes -- 5.2.1.C[∞]-rings -- 5.2.2.C[∞]-schemes -- 5.2.3.Modules over C[∞]-rings, and cotangent modules --
Contents note continued: 5.2.4.Quasicoherent sheaves on C[∞]-schemes -- 5.3.The 2-category of d-spaces -- 5.3.1.The definition of d-spaces -- 5.3.2.Gluing d-spaces by equivalences -- 5.3.3.Fibre products in dSpa -- 5.4.The 2-category of d-manifolds -- 5.4.1.The definition of d-manifolds -- 5.4.2.̀Standard model' d-manifolds, 1- and 2-morphisms -- 5.4.3.The 2-category of virtual vector bundles -- 5.4.4.Equivalences in dMan, and gluing by equivalences -- 5.4.5.Submersions, immersions and embeddings -- 5.4.6.D-transversality and fibre products -- 5.4.7.Embedding d-manifolds into manifolds -- 5.4.8.Orientations on d-manifolds -- 5.4.9.D-manifolds with boundary and corners, d-orbifolds -- 5.4.10.D-manifold bordism, and virtual cycles -- 5.4.11.Relation to other classes of spaces in mathematics -- A.Basics of 2-categories -- 6.13/2 ways of counting curves / R. P. Thomas -- 0.Introduction -- 1/2.Naive counting of curves -- 1 1/2 Gromov--Witten theory --
Contents note continued: 2 1/2 Gopakumar--Vafa / BPS invariants -- 3 1/2 Donaldson-Thomas theory -- 4 1/2 Stable pairs -- 5 1/2 Stable unramified maps -- 6 1/2 Stable quotients.
Other author Brambila, L. (Leticia), editor.
García-Prada, O. (Oscar), 1960- editor.
Newstead, P. E., editor.
Thomas, Richard P. W., editor.
Subject Moduli theory.
Geometry, Algebraic.
Moduli theory -- Congresses.
ISBN 9781107636385 (paperback)