Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)

SIGMA 17 (2021), 068, 66 pages      arXiv:1902.08298      https://doi.org/10.3842/SIGMA.2021.068
Contribution to the Special Issue on Primitive Forms and Related Topics in honor of Kyoji Saito for his 77th birthday

Good Wild Harmonic Bundles and Good Filtered Higgs Bundles

Takuro Mochizuki
Research Institute for Mathematical Sciences, Kyoto University, Kyoto 606-8502, Japan

Received July 16, 2020, in final form June 28, 2021; Published online July 17, 2021

Abstract
We prove the Kobayashi-Hitchin correspondence between good wild harmonic bundles and polystable good filtered $\lambda$-flat bundles satisfying a vanishing condition. We also study the correspondence for good wild harmonic bundles with the homogeneity with respect to a group action, which is expected to provide another way to construct Frobenius manifolds.

Key words: wild harmonic bundles; Higgs bundles; $\lambda$-flat bundles; Kobayashi-Hitchin correspondence.

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