Source: Dissertation Abstracts International, Volume: 79-10(E), Section: B.
Advisors: Tony Pantev Committee members: Jonathan Block; Ron Donagi.
Özet:
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 and Donagi-Pantev-Simpson.