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