The blowup of a complex surface at a point is one of the most basic birational operation in algebraic geometry. It replaces a point by a projective line. In topology, it corresponds to making the connected sum with the projective plane with the opposite orientation. The relation between moduli spaces of coherent sheaves (vector bundles with singularities) on the original surface and on the blowup surface is of our interest. In this talk, I will explain that two moduli spaces can be understood via the `wall-crossing', i.e., a change of the stability parameters. Hence two moduli spaces are connected by a sequence of birational operations. (Joint work with Kota Yoshioka)

nakajima@math.kyoto-u.ac.jp