Teichmuller space and its representation with the period mapping

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Date
2016
Authors
Akhtariiev, Mykhailo
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Abstract
In this thesis, we investigate the period mapping of Teichmuller space into the Siegel upper half space. This is constructed from integrals of a basis of holomorphic one-forms along closed curves of a basis of the Riemann surface.  We consider the Riemann, Teichmuller and Torelli moduli spaces and their representation in the Siegel upper half space, and its relation to orbits of a symplectic and a set of positive polarizations of a vector space of dimension equal to the genus of the surface.
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Keywords
Mathematics, Teichmuller space, Torelli space, Riemann space, Period mapping, Teichmuller theory
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