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Examples of dHYM connections in a variable background

Part of: Complex manifolds Global differential geometry

Published online by Cambridge University Press:  02 October 2023

Enrico Schlitzer  and
Jacopo Stoppa
Enrico Schlitzer
Affiliation:
Independent Scholar, Bologna, Italy e-mail: [email protected]
Jacopo Stoppa*
Affiliation:
Area Matematica, SISSA, Trieste, Italy
*
e-mail: [email protected]
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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, realization as B-branes, the small radius limit, and canonical representatives of complexified Kähler classes.

Keywords

Deformed Hermitian Yang–Mills connectionsscalar curvatureruled surfaces

MSC classification

Primary: 53C55: Hermitian and Kählerian manifolds
Secondary: 32Q15: Kähler manifolds 32Q26: Notions of stability
Type
Article
Information
Canadian Journal of Mathematics , Volume 76 , Issue 5 , October 2024 , pp. 1609 - 1637
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Copyright
© The Author(s), 2023. Published by Cambridge University Press on behalf of The Canadian Mathematical Society

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