摘要翻译:
本文研究了有限群商$$w_r=\{(x,y,z,t)xy-z^{2r}+t^2=0}/\mu_r(a,-a,1,0),r\geq1,$$的奇异锥面的辛几何,我们称之为Orbi-conifolds。构造了相关的orbifold辛针叶跃迁和orbifold辛flop。设$X$和$Y$是两个辛轨道,由这样一个翻牌连接起来。研究了$X$和$Y$上例外类的orbifold Gromov-Witten不变量,证明了它们具有同构的阮上同调。因此,我们验证了阮的一个猜想。
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英文标题:
《Singular symplectic flops and Ruan cohomology》
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作者:
Bohui Chen, An-Min Li, Qi Zhang, Guosong Zhao
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最新提交年份:
2008
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分类信息:
一级分类:Mathematics 数学
二级分类:Symplectic Geometry 辛几何
分类描述:Hamiltonian systems, symplectic flows, classical integrable systems
哈密顿系统,辛流,经典可积系统
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一级分类:Mathematics 数学
二级分类:Algebraic Geometry 代数几何
分类描述:Algebraic varieties, stacks, sheaves, schemes, moduli spaces, complex geometry, quantum cohomology
代数簇,叠,束,格式,模空间,复几何,量子上同调
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英文摘要:
In this paper, we study the symplectic geometry of singular conifolds of the finite group quotient $$ W_r=\{(x,y,z,t)|xy-z^{2r}+t^2=0 \}/\mu_r(a,-a,1,0), r\geq 1, $$ which we call orbi-conifolds. The related orbifold symplectic conifold transition and orbifold symplectic flops are constructed. Let $X$ and $Y$ be two symplectic orbifolds connected by such a flop. We study orbifold Gromov-Witten invariants of exceptional classes on $X$ and $Y$ and show that they have isomorphic Ruan cohomologies. Hence, we verify a conjecture of Ruan.
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PDF链接:
https://arxiv.org/pdf/0804.3144