We study Higgs branch localization of N=2 supersymmetric theories placed on
compact Euclidean manifolds. We analyze the resulting localization equations in
detail on the four-sphere and find that in this case the path integral is
dominated by vortex-like configurations as well as singular Seiberg-Witten
monopoles located at the north and south pole. The partition function is
written accordingly.Comment: 37 pages; v2: minor typos corrected, published versio