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.
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)
关键词
奇异
混合型
猜想
仿射超曲面
定位技术
切削参数
触发器
上同调
Ruan＇s conjecture, singular symplectic flops, （r, b）-orbiconifold singularity, Ruan cohomology,virtual localization
