| Summary: | <p> This thesis contains two parts. </p><p> In the first part, we will give the Deligne 1-motives up to isogeny corresponding to the <b>Q</b>-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. </p><p> In the second part, we study the nonableian Hodge theory for nodal curves, construct a “Dolbeault moduli spaces” M<sub>Dol</sub>(<i> X,m</i>) 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 M<sub>Dol</sub>(<i>X,m</i>) and the mixed Hodge structure on <b>C</b><sup>*</sup>-fixed points in M<sub>Dol</sub>(<i>X,m</i>).</p><p>
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