Kaleb Ruscitti, University of Waterloo
Embedding a family of moduli spaces of SL(2,C) bundles into projective spaces
The moduli space of polystable degree-0 SL(2,C) bundles on a compact connected Riemann surface of genus g>=2 is a Kähler manifold, and an open subset of the moduli space of semi-stable bundles, which is a projective variety of dimension 3g-3. Biswas and Hurtubise constructed a toric degeneration of this moduli space, meaning a family of moduli spaces over C whose fiber over 0 is a toric variety. The toric variety has a moduli interpretation as a space of framed parabolic bundles.
In this talk, I will describe the family and then describe how one can embed the entire family into P^N x C. This is the key step in a current project I am working on, about relating different geometric quantizations of the moduli space of SL(2,C) bundles.
MC 5403