Good Wild Harmonic Bundles and Good Filtered Higgs Bundles

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.

References in corpus (7)

• Asymptotic behaviour of tame harmonic bundles and an application to pure twistor $D$-modules
• Kobayashi-Hitchin correspondence for tame harmonic bundles and an application
• Asymptotic behaviour of variation of pure polarized TERP structures
• tt*-geometry in quantum cohomology
• Conformal limits and the Bialynicki-Birula stratification of the space of lambda-connections
• Non-Abelian Hodge Theory and Related Topics
• Simpson-Mochizuki Correspondence for $\lambda$-Flat Bundles

Cited by in corpus (4)

• Harmonic metrics of generically regular semisimple Higgs bundles on non-compact Riemann surfaces
• Triply Periodic Monopoles and Difference Modules on Elliptic Curves
• The Ooguri-Vafa Space as a Moduli Space of Framed Wild Harmonic Bundles
• Dual boundary complexes of Betti moduli spaces over the two-sphere with one irregular singularity