Deformations of holomorphic-Higgs pairs
Takashi Ono
TL;DR
This paper investigates the deformation theory of holomorphic-Higgs pairs, introducing a DGLA framework, deriving the governing Maurer-Cartan equation, and constructing a locally complete Kuranishi family.
Contribution
It develops a DGLA-based approach to deformations of holomorphic-Higgs pairs and establishes the local completeness of the associated Kuranishi family.
Findings
Derived the Maurer-Cartan equation for deformations
Constructed the Kuranishi family of holomorphic-Higgs pairs
Proved the local completeness of the deformation space
Abstract
We study the deformation of the holomorphic-Higgs pair. The holomorphic-Higgs pair is a pair of a complex manifold and a Higgs bundle over it. We introduce the differential graded Lie algebra (DGLA) which comes from the deformation. We derive the Maurer-Cartan equation which governs the deformation of the holomorphic-Higgs pair, construct the Kuranishi family of it, and prove its local completeness.
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Taxonomy
TopicsAdvanced Topics in Algebra · Nonlinear Waves and Solitons · Homotopy and Cohomology in Algebraic Topology