Generalized Deligne-Hitchin Twistor Spaces: Construction and Properties
arXiv:2010.06893 · doi:10.1016/j.bulsci.2024.103396
Abstract
In this paper, we generalize the construction of Deligne-Hitchin twistor space by gluing two certain Hodge moduli spaces. We investigate such generalized Deligne-Hitchin twistor space as a complex analytic manifold. More precisely, we show it admits holomorphic sections with weight-one property and semi-negative energy, and it carries a balanced metric, and its holomorphic tangent bundle (for the case of rank one) is stable. Moreover, we also study the automorphism groups of the Hodge moduli spaces and the generalized Deligne-Hitchin twistor space.
Final version, fix a mistake, comments welcome!
References in corpus (13)
- Kobayashi-Hitchin correspondence for tame harmonic bundles II
- L^2 cohomology of hyperkähler quotients
- Duality and Fibrations on G_2 Manifolds
- Very stable Higgs bundles, equivariant multiplicity and mirror symmetry
- On moduli spaces of Hitchin pairs
- Classification of the automorphism and isometry groups of Higgs bundle moduli spaces
- Torelli theorem for the Deligne--Hitchin moduli space
- Real holomorphic sections of the Deligne-Hitchin twistor space
- Energy of sections of the Deligne-Hitchin twistor space
- Non-Abelian Hodge Theory and Related Topics
- Simpson Filtration and Oper Stratum Conjecture
- On the Automorphisms of a Rank One Deligne-Hitchin Moduli Space
- Stability and Hermitian-Einstein metrics for vector bundles on framed manifolds