CEU Electronic Theses and Dissertations, 2018
| Author | Máté, Bálint Ádám |
|---|---|
| Title | Logarithmic Hodge Theory on Line Bundles |
| Summary | This thesis intends to serve as an introduction to Hodge theory in the simplest possible setting: our base manifold is a compact Riemann surface Σ without boundary, the vector bundle E → Σ is the trivial complex line bundle. In this setup the Betti, the de Rham and the Dolbeault groupoids are introduced and their equivalence is investigated. The proof of the equivalence of the de Rham and Dolbeault groupoids uses the existence of harmonic metrics with respect to a connection D on E. The thesis concludes with the generalisation of the existence of such metrics to the case where the connection is no longer smooth but has logarithmic singularities, and the weight of the associated local system vanishes. |
| Supervisor | Szabó Szilárd |
| Department | Mathematics MSc |
| Full text | https://www.etd.ceu.edu/2018/mate_balint.pdf |
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