2008-08-012024-05-17https://scholars.lib.ntu.edu.tw/handle/123456789/694806摘要：這個計劃的主要目的是要去探討比較在一般ordinary flops 中，它們的 quantum cohomology 的不變性。我們已經知道對於 ordinary flops，它們的 Chow motives 是同構的，這說明它們的整上同調羣是同構的，但從simple flops的經驗中知道它們的整上同調環有不同的乘法結構，仿照 simple的情形，我們希望也可以在一般 ordinary flops 之下確切得到它們乘法結構的誤差公式，並在quantum product 中彌補這個誤差，並期望證明在一般 ordinary flops之下的 big quantum cohomology 是不變的。 另外，quantum product 僅用到了genus 0 的 Gromov-Witten 不變量，因此我們也希望能進一步探討 higher genus Gromov-Witten 不變量在 ordinary flops 之下的不變性。<br> Abstract: The aim of this research is to understand the invariance of quantum cohomology under general ordinary flops. We have shown that for an ordinary flop, the graph closure induces an isomorphism between their Chow motives. The Chow motives certainly imply the universal cohomology theory, so their integral cohomology groups are isomorphic under the graph closure. The problem is that the ring structures of their cohomology are different. For simple ordinary flops, we have shown that their big quantum cohomology rings are invariant. The main goal of this project is to prove the invariance for general ordinary flops. The big quantum product in fact uses only the genus zero Gromov-Witten invariants, hence it is an interesting problem to ask whether the higher genus invariants are also invariant under the graph correspondence for ordinary flops. The second main goal of this project is to treat this problem at least for the case of simple ordinary flops.ordinary flopsGromov-Witten 不變量ordinary flopsGromov-Witten invariants量子同調環的不變性