Limiting Mixed Hodge Theory and Nonabelian Hodge Theory for Nodal Curves
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).
Degree
Ph.D.
Advisors
Arapura, Purdue University.
Subject Area
Mathematics
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