![](/__local/9/24/29/6337A60741E1F44B52506F945EC_C5F53482_67C1C.png)
Title:Blowup Formula of Genus Zero Gromov-Witten Invariants along Positive Center
主讲人:杜承勇(四川师范大学)
Abstract:In this talk we will introduce our recent work on blowup formula of genus zero Gromov--Witten invariants. Let S be a smooth subvariety of a smooth projective variety X, and Y be the blowup of X along S. The blowup, W, of X×ℙ^1 along S×0 is a birational cobordism between X and Y. The natural S^1 action on ℙ^1 lifts to an action on W, with fixed loci: X, Y, S_*. By taking r-th root over W along Y with r⋙ 1, via virtual localization technique and Pixton's polynomiality of certain twisted Gromov--Witten invariants on r, when the normal bundle of S in X is positive in the sense of Riemann--Roch index, we proved a blowup formula of genus zero Gromov--Witten invariants that identifies the natural corresponded invariants of X and Y. When the normal bundle is just nonnegative, there would be a correction term from the invariant of S. As applications, our formulae imply that the symplectic k-point rationally connectedness is preserved by blowups along centers with positive normal bundles. This talk is based on a joint work with Bohui Chen.
时间:4月19日(周五)9:00-11:00
地点:中心校区知新楼B1032
邀请人:王新