Date of Award

2018

Degree Type

Dissertation

Degree Name

Doctor of Philosophy (PhD)

Graduate Group

Mathematics

First Advisor

Tony Pantev

Abstract

We study the spectral data for the higher direct images of a parabolic Higgs

bundle along a map between a surface and a curve with both vertical and horizontal

parabolic divisors. We describe the cohomology of a parabolic Higgs bundle on a

curve in terms of its spectral data. We also calculate the integral kernel that

reproduces the spectral data for the higher direct images of a parabolic Higgs bundle

on the surface. This research is inspired by and extends the works of Simpson [21]

and Donagi-Pantev-Simpson [7].

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Mathematics Commons

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