Examples of dHYM connections in a variable background

Abstract

We study deformed Hermitian Yang-Mills (dHYM) connections on ruled surfaces explicitly, using the momentum construction. As a main application we provide many new examples of dHYM connections coupled to a variable background Kähler metric. These are solutions of the moment map partial differential equations given by the Hamiltonian action of the extended gauge group, coupling the dHYM equation to the scalar curvature of the background. The large radius limit of these coupled equations is the Kähler-Yang-Mills system of Álvarez-Cónsul, Garcia-Fernandez and García-Prada, and in this limit our solutions converge smoothly to those constructed by Keller and Tønnesen-Friedman. We also discuss other aspects of our examples including conical singularities, realisation as B-branes, the small radius limit and canonical representatives of complexified Kähler classes.

33 pages, 2 figures

References in corpus (5)

• Deformed Hermitian Yang-Mills connections, extended gauge group and scalar curvature
• Collapsing of the line bundle mean curvature flow on Kähler surfaces
• Stability and the deformed Hermitian-Yang-Mills equation
• Tan-concavity property for Lagrangian phase operators and applications to the tangent Lagrangian phase flow
• Chern number inequalities of deformed Hermitian-Yang-Mills metrics on four dimensional Kaehler manifolds