Dissertation/Thesis Abstract

Limiting Mixed Hodge Theory and Nonabelian Hodge Theory for Nodal Curves
by Hao, Feng, Ph.D., Purdue University, 2018, 92; 10844977
Abstract (Summary)

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).

Indexing (document details)
Advisor: Arapura, Donu
School: Purdue University
Department: Mathematics
School Location: United States -- Indiana
Source: DAI-B 80/01(E), Dissertation Abstracts International
Subjects: Mathematics
Keywords: Limiting mixed hodge theory, Nodal curves, Nonabelian hodge theory
Publication Number: 10844977
ISBN: 9780438369115
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