Date of Award
8-2018
Degree Type
Dissertation
Degree Name
Doctor of Philosophy (PhD)
Department
Mathematics
Committee Chair
Donu Arapura
Committee Member 1
Kenji Matsuki
Committee Member 2
Deepam Patel
Committee Member 3
Tong Liu
Abstract
This thesis contains two parts. In the first part, we will give the Deligne 1-motives up to isogeny corresponding to the Q-limit mixed Hodge structures of semi-stable degenerations of curves, using logarithmic structures and Steenbrink’s cohomological mixed Hodge complexes associated to semi-stable degenerations of curves. In the second part, we study the nonableian Hodge theory for nodal curves, construct a “Dolbeault moduli spaces” MDol(X,m) for Higgs bundles on nodal curves, and give the formality theorem for local systems and Higgs bundles on nodal curves. We also give some discussions on the Hitchin fibration of MDol(X,m) and the mixed Hodge structure on C∗-fixed points in MDol(X,m).
Recommended Citation
Hao, Feng, "Limiting Mixed Hodge Theory and Nonabelian Hodge Theory for Nodal Curves" (2018). Open Access Dissertations. 1945.
https://docs.lib.purdue.edu/open_access_dissertations/1945