Orbifold Gromov-Witten theory of weighted blowups  

作　　者：Bohui Chen Cheng-Yong Du Rui Wang 

机构地区：[1]Department of Mathematics and Yangtze Center of Mathematics,Sichuan University,Chengdu 610064,China [2]School of Mathematical Sciences and V.C.&V.R.Key Lab,Sichuan Normal University,Chengdu 610068,China [3]Department of Mathematics,University of California,Berkeley,Berkeley,CA 94720,USA

出　　处：《Science China Mathematics》2020年第12期2475-2522,共48页中国科学：数学（英文版）

基　　金：supported by National Natural Science Foundation of China(Grant Nos.11890663,11821001,11826102 and 11501393);the Sichuan Science and Technology Program(Grant No.2019YJ0509);a joint research project of Laurent Mathematics Research Center of Sichuan Normal University and V.C.&V.R.Key Lab of Sichuan Province。

摘　　要：Consider a compact symplectic sub-orbifold groupoid S of a compact symplectic orbifold groupoid(X,ω).LetXabe the weight-a blowup of X along S,and Da=PNa be the exceptional divisor,where N is the normal bundle of S in X.In this paper we show that the absolute orbifold Gromov-Witten theory ofXacan be effectively and uniquely reconstructed from the absolute orbifold Gromov-Witten theories of X,S and Da,the natural restriction homomorphism HCR^*(X)→HCR*(S)and the first Chern class of the tautological line bundle over DQ.To achieve this we first prove similar results for the relative orbifold Gromov-Witten theories of(Xa|Da)and(Na|Da).As applications of these results,we prove an orbifold version of a conjecture of Maulik and Pandharipande(Topology,2006)on the Gromov-Witten theory of blowups along complete intersections,a conjecture on the Gromov-Witten theory of root constructions and a conjecture on the Leray-Hirsch result for the orbifold Gromov-Witten theory of Tseng and You(J Pure Appl Algebra,2016).

关 键 词：orbifold Gromov-Witten theory Leray-Hirsch result weighted projective bundle weighted blowup root stack blowup along complete intersection 

分 类 号：O187[理学—数学]