Moduli spaces of vector bundles on toric surfaces
The moduli spaces parametrizing isomorphism classes of vector bundles are poorly understood. For certain choices of the first Chern class and a suitable second Chern class, we show that there exists an ample line bundle on a smooth complete toric surface for which the moduli space of rank two vector bundles is isomorphic to projective space. For the other choices of the first Chern class, we demonstrate with an example that the moduli space can still be isomorphic to projective space. To compute the topological Euler characteristic of a moduli space of rank two vector bundles, we look at its set of torus-fixed points and give it an interpretation in terms of the torus-equivariant vector bundles. Using a correspondence between collections of filtrations and torus-equivariant vector bundles given in [Kly89], we interpret the torus-fixed points of the moduli space as configurations of points on the projective line. We use this configuration to compute Euler characteristics of moduli spaces on a Hirzebruch surface.
URI for this recordhttp://hdl.handle.net/1974/24812
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