Non-Abelian Hodge Theory and Related Topics

Huang, Pengfei

doi:10.3842/sigma.2020.029

Cited by 5 publications

(2 citation statements)

References 55 publications

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“…In particular, he explained that the Kobayashi-Hitchin correspondences for λ-flat bundles can be studied in a unified way [64]. For more recent study on the moduli spaces of λ-connections, see [10,26,27,67], for example.…”

Section: Higgs Bundles and λ-Flat Bundlesmentioning

confidence: 99%

Good Wild Harmonic Bundles and Good Filtered Higgs Bundles

Mochizuki

2021

SIGMA

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Section: Higgs Bundles and λ-Flat Bundlesmentioning

confidence: 99%

Good Wild Harmonic Bundles and Good Filtered Higgs Bundles

Mochizuki

2021

SIGMA

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“…The corresponding twistor space M DH (Σ, G) is known as the Deligne-Hitchin moduli spaces [44]. These spaces M DH (Σ, G) have been the topic of many papers in recent years; see for example [10,32,33,15,16] and [5,6,4,24,25] and references therein.…”

Section: Introductionmentioning

confidence: 99%

Geometry of the space of sections of twistor spaces with circle action

Beck,

Biswas,

Heller

et al. 2021

Preprint

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We study the holomorphic symplectic geometry of (the smooth locus of) the space of holomorphic sections of a twistor space with rotating circle action. The twistor space has a meromorphic connection constructed by Hitchin. We give an interpretation of Hitchin's meromorphic connection in the context of the Atiyah-Ward transform of the corresponding hyperholomorphic line bundle. It is shown that the residue of the meromorphic connection serves as a moment map for the induced circle action, and its critical points are studied. Particular emphasis is given to the example of Deligne-Hitchin moduli spaces. Contents 1.2. Space of holomorphic sections as a complexified hyperkähler manifold 1.3. Alternative description of the holomorphic symplectic form Ω x on S ′ 2. The hyperholomorphic line bundle and the energy functional 2.1. Rotating circle actions and the hyperholomorphic line bundle 2.2. The S 1 -action on S and the energy functional 2.3. Critical Points of E 2.4. The Atiyah-Ward transform of L Z 2.5. The Atiyah-Ward transform and the meromorphic connection 2.6. An alternative construction of Hitchin's meromorphic connection 3. Space of holomorphic sections of the Deligne-Hitchin moduli space 3.1. Hitchin's self-duality equations 3.2. The Deligne-Hitchin moduli space 3.3. The line bundle on M irr DH 3.4. Irreducible and admissible sections 4. Energy functional on sections of the Deligne-Hitchin moduli space 4.1. The energy as a moment map 4.2. Explicit description of some C * -fixed sections 4.3. The energy of a C * -fixed section 4.4. The second variation of the Energy at a C * -fixed section 4.5. Sections and the degree of the hyperholomorphic line bundle References

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Simpson filtration and oper stratum conjecture

Huang

2021

manuscripta math.

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Non-Abelian Hodge Theory and Related Topics

Cited by 5 publications

References 55 publications

Good Wild Harmonic Bundles and Good Filtered Higgs Bundles

Good Wild Harmonic Bundles and Good Filtered Higgs Bundles

Geometry of the space of sections of twistor spaces with circle action

Simpson filtration and oper stratum conjecture

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