A genus-two Riemann surface admits a canonical decomposition into Dirichlet polygons determined by its six Weierstrass points. All possible associated graphs are determined explicitly from circle packing problems, solved by systems of linear inequalities whose solutions determine a finite 6-dimensional polyhedral complex in 12-dimensional space. The 6-dimensional Moduli Space of genus-two Riemann surfaces inherits a canonical explicit decomposition into Euclidean polyhedra, giving new natural coordinates for the Teichmuller Space of all possible constant curvature geometries on a marked genus-two surface.
| Identifer | oai:union.ndltd.org:ADTP/245419 |
| Date | January 2007 |
| Creators | Amaris, Armando Jose Rodado |
| Source Sets | Australiasian Digital Theses Program |
| Language | English |
| Detected Language | English |
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