Kaleb D. Ruscitti, Department of Pure Mathematics, University of Waterloo
"Understanding the local behaviour of a toric degeneration of the moduli of holomorphic bundles"
There is a toric degeneration of the moduli space of holomorphic semi-stable rank 2 bundles on a Riemann surface, induced by a degeneration of the Riemann surface along 2g-2 loops. Biswas and Hurtubise gave an explicit local description of this degeneration in terms of the connection matrices that define the holomorphic structure on the bundles.
In this talk, I will discuss my ongoing project to understand how the functions on the moduli space behave under this degeneration. I will begin by reviewing the relationship between sections of bundles on toric varieties and lattice points in their moment polytopes. Then I will try to use this theory to work out explicitly what happens to functions in the case of the toric degeneration for the aforementioned moduli space.
MC 5417