Generalized Deligne–Hitchin twistor spaces: Construction and properties

Abstract

In this paper, we generalize the construction of Deligne–Hitchin twistor space by gluing two certain Hodge moduli spaces. We investigate some properties of such generalized Deligne–Hitchin twistor space as a complex analytic manifold. More precisely, we show it admits holomorphic sections whose normal bundle contains a semistable subbundle with positive degree and whose energy is semi-negative, and it carries a balanced metric. Moreover, we also study the automorphism groups of the Hodge moduli spaces and the generalized Deligne–Hitchin twistor spaces.