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].
Recommended Citation
Jin, Xiaofei, "Spectral Data For L^2 Cohomology" (2018). Publicly Accessible Penn Dissertations. 2815.
https://repository.upenn.edu/edissertations/2815