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Descripción del Curso
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This are the notes of a seminar talk delivered in summer 2008 at Bonn. Let SU (2, 1) be the moduli space of rank 2 bundles with a fixed determinant of rank 1 over a curve C of genus g ≥ 2. This is a Fano manifold of Picard rank 1. We discuss the example g = 2 where SU (2, 1) is the intersection of two quadrics in P5 . In this case the minimal rational curves are lines. There is a very interesting class of rational curves on SU (2, 1), called Hecke curves, which are constructed by extending a given bundle by torsion sheaves. In the case g ≥ 3 we will see that Hecke curves have minimal anti-canonical degree (4) and that any rational curve passing through a generic point is a Hecke curve.
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Hecke Curves and Moduli spcaes of Vector Bundles
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