On the Connectedness of the Real Part of Moduli Spaces of Vector Bundles on Real Algebraic Surfaces

摘要

Let X be a smooth projective surface with q(X) = 0 defined over R and M(X;r;c1;c2;H) the moduli space of H-stable rank r vector bundles on X with Chern classes c1 and c2. Assume either r = 3 and X(R) connected or r = 3 and X(R) =?? or r=2 and X(R) = ??. We prove that quite often M is connected.