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 such generalized Deligne-Hitchin twistor space as a complex analytic manifold, more precisely, we show it admits a global smooth trivialization such that the induced product metric is balanced, and it carries a semistable holomorphic tangent bundle. Moreover, we study the automorphism groups of the Hodge moduli spaces and the generalized Deligne-Hitchin twistor space.