부산대학교 도서관

The author uses cosection localization, a fundamental technique in enumerative algebraic geometry, to show that the virtual fundamental cycle $[\roman{Quot}_S^l({\Cal E})]^{\roman{vir}}$ 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 explicitly localized 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 the author to obtain a structure theorem for virtual tautological integrals over $[\roman{Quot}_S^l({\Cal E})]^{\roman{vir}}$, a direct analogue of a prior result of Ellingsrud, Göttsche and Lehn, and give geometric proofs of statements about the virtual Euler characteristic, virtual Segre series and virtual tautological integrals of line bundles on $\roman{Quot}_S^l({\Cal E})$, using recent results by Oprea and Pandharipande et al.