Abstract
Recently there has been a renewed interest in Donaldson invariants and Seiberg–Witten invariants due to the influx of virtual intersection theory. See Mochizuki [15], Gottsche, Nakajima and Yoshioka [6], and [4], for instance. The purpose of this paper is to prove a conjecture (Theorem 1.1 below) of Durr, Kabanov and Okonek in [4], which provides a natural algebro-geometric theory of Seiberg–Witten invariants. Our main technique is the cosection localization principle in Kiem and Li [8] that effectively localizes the virtual cycle when there is a cosection of the obstruction sheaf.
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