Sorvali Dilatation and Spin Divisors on Riemann and Klein Surfaces
We review the Sorvali dilatation of isomorphisms of covering groups of Riemann surfaces and extend the definition to groups containing glide-reflections. Then we give a bound for the distance between two surfaces, one of them resulting from twisting the other at a decomposing curve. Furthermore, we...
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| Format: | Others |
| Language: | English English |
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Florida State University
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| Online Access: | http://purl.flvc.org/fsu/fd/FSU_SUMMER2017_ALMALKI_fsu_0071E_14064 |
| Summary: | We review the Sorvali dilatation of isomorphisms of covering groups of Riemann surfaces and extend the definition to groups containing glide-reflections. Then we give a bound for the distance between two surfaces, one of them resulting from twisting the other at a decomposing curve. Furthermore, we study spin structures on Riemann and Klein surfaces in terms of divisors. In particular, we take a closer look at spin structures on hyperelliptic and p-gonal surfaces defined by divisors supported on branch points. Moreover, we study invariant spin divisors under automorphisms and anti-holomorphic involutions of Riemann surfaces. === A Dissertation submitted to the Department of Mathematics in partial fulfillment of the requirements for the degree of Doctor of Philosophy. === Summer Semester 2017. === July 19, 2017. === divisors, Klein, Riemann, Sorvali, Spin, Teichmuller === Includes bibliographical references. === Craig A. Nolder, Professor Directing Dissertation; Fred Huffer, University Representative; Eric Klassen, Committee Member; Mark Van Hoeij, Committee Member. |
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