Ruan's conjecture on singular symplectic flops of mixed type  

作　　者：CHEN BoHui LI AnMin LI XiaoBin ZHAO GuoSong 

机构地区：[1]Yangtze Center of Mathematics,Department of Mathematics,Sichuan University [2]Department of Mathematics,Southwest Jiaotong University [3]Department of Mathematics,Sichuan University

出　　处：《Science China Mathematics》2014年第6期1121-1148,共28页中国科学：数学（英文版）

基　　金：supported by National Natural Science Foundation of China (Grant Nos. 11171235,11071176,11071173 and 11221101);Specialized Research Fund for the Doctoral Program of Higher Education (Grant No. 20100181110071);the Fundamental Research Funds for the Central Universities of China (Grant No. SWJTU12BR028)

摘　　要：In this paper,we study the global singular symplectic flops related to the following affine hypersurface with cyclic quotient singularities,Vr,b={(x,y,z,t)∈C4|xy-z2r+t2=0}/μr(a,-a,b,0),r 2,where b=1 appears in Mori’s minimal model program and b=1 is a new class of singularities in symplectic birational geometry.We prove that two symplectic 3-orbifolds which are singular flops to each other have isomorphic Ruan cohomology rings.The proof is based on the symplectic cutting argument and virtual localization technique.In this paper, we study the global singular symplectic flops related to the following affine hypersurface with cyclic quotient singularities, Vr,b={（x,y,z,t）∈C4｜xy-z2r＋t2=0}/μr（a,-a,b,0）, r≥2, where b=1 appears in Mori＇s minimal model program and b≠1 is a new class of singularities in symplectic birational geometry. We prove that two symplectic 3-orbifolds which are singular flops to each other have isomorphic Ruan cohomology rings. The proof is based on the symplectic cutting argument and virtual localization technique.

关 键 词：Ruan＇s conjecture singular symplectic flops （r b）-orbiconifold singularity Ruan cohomology virtual localization 

分 类 号：O186.11[理学—数学]