Date of Award


Degree Type


Degree Name

Doctor of Philosophy (PhD)



Committee Chair

Donu Arapura

Committee Member 1

Kenji Matsuki

Committee Member 2

Deepam Patel

Committee Member 3

Tong Liu


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).