Spectral Data For L^2 Cohomology
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Degree type
Doctor of Philosophy (PhD)
Graduate group
Mathematics
Discipline
Subject
Higgs bundle
Monodromy weight filtration
Nonabelian Hodge theory
Parabolic L^2 Dolbeault complex
Root stack
Spectral correspondence
Mathematics
Monodromy weight filtration
Nonabelian Hodge theory
Parabolic L^2 Dolbeault complex
Root stack
Spectral correspondence
Mathematics
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License
Copyright date
2018-09-27T20:18:00-07:00
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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].
Advisor
Tony Pantev
Date of degree
2018-01-01