Mathematical Physics Seminar
Monday 12.IV.2010
Time: 16:00-17:00
Room: 0089
Instytut Matematyki, ul. Łojasiewicza 6, 30-348 Kraków
Nuno Romão
(Uniwersytet Jagielloński, Cracow, Poland)
Vortex moduli spaces and Grassmann manifolds
Abstract:
Vortices are configurations of fields for certain gauge theories on fibre bundles
over a Riemann surface Σ. For line bundles, the moduli spaces of these objects
are modelled on the space of effective divisors on Σ with a fixed degree, while
the generalisation for more complicated targets (typical fibres) is more intricate.
In my talk, I shall explain joint work with Indranil Biswas where we use Quot
schemes to give a description of the moduli spaces of vortices with targets
Matrxn(C), for n ≥ r and Σ closed.
We show that the moduli spaces embed into
Grassmannians, and this gives rise to interesting geometrical questions. In the
"local case" n=r, there is a neat description of the moduli spaces using Hecke
modifications, which I will also explain if time permits.
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