Moduli of vector bundles on higher-dimensional base manifolds — Construction and variation

DOI10.1142/S0129167X16500543zbMath1427.14027MaRDI QIDQ3188173

Daniel Greb, Matei Toma, Julius Ross

Publication date: 17 August 2016

Published in: International Journal of Mathematics (Search for Journal in Brave)

zbMATH Keywords

moduli of quiver representationswall-crossingDonaldson-Uhlenbeck compactificationsheaves on Kähler manifoldsvariation of Gieseker moduli spaces

Mathematics Subject Classification ID

Vector bundles on surfaces and higher-dimensional varieties, and their moduli (14J60) Geometric invariant theory (14L24) Moduli problems for differential geometric structures (58D27) Complex-analytic moduli problems (32G13) Algebraic moduli problems, moduli of vector bundles (14D20) Representations of quivers and partially ordered sets (16G20) Minimal model program (Mori theory, extremal rays) (14E30)

Related Items

Moduli spaces of sheaves that are semistable with respect to a Kähler polarisation, Complex algebraic compactifications of the moduli space of Hermitian Yang-Mills connections on a projective manifold, Positivity functions for curves on algebraic varieties

Cites Work

• A wall crossing formula of Donaldson-Thomas invariants without Chern-Simons functional
• Recasting results in equivariant geometry
• Compactified Jacobians and Torelli map
• Equivalence classes of polarizations and moduli spaces of sheaves
• Algebraic geometric interpretation of Donaldson's polynomial invariants
• Polynomial invariants for smooth four-manifolds
• Configurations in abelian categories. II: Ringel-Hall algebras
• A functorial construction of moduli of sheaves
• Compactifying the Picard scheme
• Fonctions différentiables invariantes sous l'opération d'un groupe réductif
• Comparison of the Donaldson polynomial invariants with their algebro- geometric analogues
• Stability for an abelian category
• Irreducibility of the punctual quotient scheme of a surface
• Walls of Gieseker semistability and the Mumford-Thaddeus principle for moduli spaces of sheaves over higher dimensional bases
• Variation of geometric invariant theory quotients. (With an appendix: ``An example of a thick wall by Nicolas Ressayre)
• A holomorphic Casson invariant for Calabi-Yau 3-folds, and bundles on \(K3\) fibrations.
• Global moduli spaces and simple holomorphic bundles
• Semistable sheaves in positive characteristic
• Gauge theory and calibrated geometry. I
• Configurations in abelian categories. III: Stability conditions and identities
• Configurations in abelian categories. IV: Invariants and changing stability conditions
• Configurations in abelian categories. I: Basic properties and moduli stacks
• Relations between the Kähler cone and the balanced cone of a Kähler manifold
• Space of unitary vector bundles on a compact Riemann surface
• Hilbert schemes and stable pairs: GIT and derived category wall crossings
• Geometric stability of the cotangent bundle and the universal cover of a projective manifold
• Rationally connected foliations after Bogomolov and McQuillan
• FAMILIES OF HOLOMORPHIC BUNDLES
• MODULI OF REPRESENTATIONS OF FINITE DIMENSIONAL ALGEBRAS
• Mumford–Thaddeus Principle on the Moduli Space of Vector Bundles on an Algebraic Surface
• VARIATION OF THE GIESEKER AND UHLENBECK COMPACTIFICATIONS
• The pseudo-effective cone of a compact Kähler manifold and varieties of negative Kodaira dimension
• Geometric invariant theory and flips