Generalized Kazdan-Warner equations associated with a linear action of a torus on a complex vector space

DOI10.1007/s10711-021-00632-zzbMath1485.53045arXiv2002.09141OpenAlexW3168779069MaRDI QIDQ2230992

Natsuo Miyatake

Publication date: 29 September 2021

Published in: Geometriae Dedicata (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2002.09141

zbMATH Keywords

geometric invariant theorymoment mapHiggs bundlesvortex equationKazdan-Warner equationcyclic Higgs bundlesperiodic Toda equation

Mathematics Subject Classification ID

Momentum maps; symplectic reduction (53D20) Methods of global Riemannian geometry, including PDE methods; curvature restrictions (53C21) PDEs on manifolds (35R01)

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Special metrics and stability for holomorphic bundles with global sections
• Katz's middle convolution algorithm
• Arbitrary N-vortex solutions to the first order Ginzburg-Landau equations
• Lie groups and Teichmüller space
• Lectures on introduction to moduli problems and orbit spaces
• The red book of varieties and schemes. Includes the Michigan lectures (1974) on ``Curves and their Jacobians.
• Hitchin-Kobayashi correspondence, quivers, and vortices
• Connectedness of Higgs bundle moduli for complex reductive Lie groups
• Adiabatic limits and Kazdan-Warner equations
• Geometry of Higgs and Toda fields on Riemann surfaces
• Cyclic Higgs bundles and the affine Toda equations
• Curvature functions for compact 2-manifolds
• On cyclic Higgs bundles
• Kostant, Steinberg, and the Stokes matrices of the tt*-Toda equations
• Nonlinear PDE aspects of the tt* equations of Cecotti and Vafa
• Vortices in holomorphic line bundles over closed Kähler manifolds
• Introduction to Toric Varieties. (AM-131)
• The Principal Three-Dimensional Subgroup and the Betti Numbers of a Complex Simple Lie Group
• The Geometry of Toric Hyperk\"ahler Varieties
• The Self-Duality Equations on a Riemann Surface
• Constructing Variations of Hodge Structure Using Yang-Mills Theory and Applications to Uniformization
• Geometric Invariant Theory
• MODULI OF REPRESENTATIONS OF FINITE DIMENSIONAL ALGEBRAS
• A Hitchin-Kobayashi correspondence for Kähler fibrations