### Abstract

Given a flat Higgs vector bundle (E, ∇, φ) over a compact connected special affine manifold, we first construct a natural filtration of E, compatible with both ∇ and φ, such that the successive quotients are polystable flat Higgs vector bundles. This is done by combining the Harder-Narasimhan filtration and the socle filtration that we construct. Using this filtration, we construct a smooth Hermitian metric h on E and a smooth one-parameter family {A_{t}}_{t∈ℝ} of ∞^{∞} automorphisms of E with the following property. Let ∇^{t} and φ^{t} be the flat connection and flat Higgs field, respectively on E constructed from ∇ and φ using the automorphism A_{t}. If θ^{t} denotes the extended connection form on E associated to the triple h, ∇^{t} and φ^{t}, then as t→ +infin;00, the connection form θ^{t} converges in the C^{∞} Frechet topology to the extended connection form θ on E given by the affine Yang-Mills-Higgs metrics on the polystable quotients of the successive terms in the above mentioned filtration. In particular, as t→ +infin;00, the curvature of θ^{t} converges in the ∞^{00} Frechet topology to the curvature of θ.

Original language | English (US) |
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Pages (from-to) | 737-754 |

Number of pages | 18 |

Journal | Communications in Analysis and Geometry |

Volume | 22 |

Issue number | 4 |

DOIs | |

State | Published - Jan 1 2014 |

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### All Science Journal Classification (ASJC) codes

- Analysis
- Statistics and Probability
- Geometry and Topology
- Statistics, Probability and Uncertainty

### Cite this

*Communications in Analysis and Geometry*,

*22*(4), 737-754. https://doi.org/10.4310/CAG.2014.v22.n4.a5