부산대학교 도서관

The author uses cosection localization, a fundamental technique inenumerative algebraic geometry, to show that the virtual fundamentalcycle $[\roman{Quot}_S^l({\Cal E})]^{\roman{vir}}$ of the Quot scheme$\roman{Quot}_S^l({\Cal E})$ of length $l$ quotients of a rank $r$,locally free sheaf $\Cal E$ on a surface $S$ can be explicitlylocalized to the virtual fundamental cycle of the Quot scheme of length$l$ quotients of the restriction ${\Cal E}|_C$ to a canonical curve $C\subset S$, which is a smooth Quot scheme. This in turn allows theauthor to obtain a structure theorem for virtual tautological integralsover $[\roman{Quot}_S^l({\Cal E})]^{\roman{vir}}$, a direct analogue ofa prior result of Ellingsrud, Göttsche and Lehn, and give geometricproofs of statements about the virtual Euler characteristic, virtualSegre series and virtual tautological integrals of line bundles on$\roman{Quot}_S^l({\Cal E})$, using recent results by Oprea andPandharipande et al.