摘要翻译：
利用Gromov-Witten理论定义了Calabi-Yau 5折叠曲线的枚举几何。我们给出了0属曲线的满足数的递推，并确定了0属曲线的移动重覆盖对1属Gromov-Witten不变量的贡献。由此得到的不变量，推测是积分的，类似于先前定义的Calabi-Yau 3和4折叠的BPS计数。我们在出现新问题的更高层面上评论局势。考虑了两个主要例子：具有平衡法束3O(-1)的局部Calabi-Yau P^2和P^6中的紧Calabi-Yau超曲面X_7。在前一种情况下，我们的整数不变量的封闭形式已经由G.Martin推测出来。在后一种情况下，我们在低程度上恢复了Ellingsrud和Stromme对椭圆曲线的经典枚举。
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英文标题：
《Enumerative Geometry of Calabi-Yau 5-Folds》
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作者：
R. Pandharipande and A. Zinger
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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：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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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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英文摘要：
  Gromov-Witten theory is used to define an enumerative geometry of curves in Calabi-Yau 5-folds. We find recursions for meeting numbers of genus 0 curves, and we determine the contributions of moving multiple covers of genus 0 curves to the genus 1 Gromov-Witten invariants. The resulting invariants, conjectured to be integral, are analogous to the previously defined BPS counts for Calabi-Yau 3 and 4-folds. We comment on the situation in higher dimensions where new issues arise.   Two main examples are considered: the local Calabi-Yau P^2 with balanced normal bundle 3O(-1) and the compact Calabi-Yau hypersurface X_7 in P^6. In the former case, a closed form for our integer invariants has been conjectured by G. Martin. In the latter case, we recover in low degrees the classical enumeration of elliptic curves by Ellingsrud and Stromme.
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PDF链接：
https://arxiv.org/pdf/0802.1640