부산대학교 도서관

Let ε be a locally free sheaf of rank r on a smooth projective surface S. The Quot scheme QuotSl(ε) of length l coherent sheaf quotients of E is a natural higher-rank generalization of the Hilbert scheme of l points of S. We study the virtual intersection theory of this scheme. If C⊂S is a smooth canonical curve, we use cosection localization to show that the virtual fundamental class of QuotSl(ε) is (-1)l times the fundamental class of the smooth subscheme Quotl C(E|C) ⊂QuotSl(ε). We then prove a structure theorem for virtual tautological integrals over QuotSl(ε). From this, we deduce, among other things, the equality of virtual Euler characteristics χvir(QuotSl(ε))=χvir(QuotSl(O⊕r)). [ABSTRACT FROM AUTHOR]