Title：Construction of Deligne - Hitchin twistor spaces via nonabelian Hodge correspondence
Speaker：Pengfei Huang（Universität Heidelberg）
Time：14:00-15:30, November19
Location：Tecent Meeting, Tecent Meeting ID: 712 157 865
Abstract：In the late 1980s, Hitchin et al. gave the construction of twistor spaces associated to each hyperKähler manifold, the original idea can be dated back to Penrose's non-linear graviton construction in 1970s. Topologically, the twistor space associated to a hyperKähler manifold is just the product of the manifold with the 2-sphere, it admits a tautological complex structure induced from the natural complex structure of the 2-sphere and the complex structure on each fiber of the product. One important reason for the study of twistor spaces is the encoding of the hyperKähler structure from holomorphic data of the twistor space. In 1990s, Deligne-Simpson interpreted Hitchin's twistor space associated to the moduli space of solutions to Hitchin's self-duality equations via the nonabelian Hodge correspondence, namely they showed such Hitchin twistor space can be described as the gluing of two certain moduli spaces. The obtained twistor space is called the Deligne-Hitchin twistor space. In this talk, I will introduce a generalization of their construction by gluing two more general moduli spaces. In the first part of the talk, I will introduce the nonabelian Hodge theory from two sides, one is the nonabelian analogue of Hodge theory, the other one is the generalization of Narasimhan-Seshadri correspondence. I will go through these theories with more details. After these background settings, I will introduce a more general construction of twistor spaces via the nonabelian Hodge correspondence, the Deligne-Hitchin twistor space appears as a special example. Based on a joint work with Prof. Zhi Hu and Prof. Runhong Zong.
