摘要翻译:
对于一个非奇异射影3重$X$,我们定义了整数不变量,实际上枚举了对$(C,D)$,其中$C\子集X$是一条嵌入曲线,$D\子集C$是一个除数。通过将一对作为派生类别$x$中的对象来查看,在关联的模空间上构造一个虚拟类。得到的不变量,经过普遍变换后,猜想等价于$x$的Gromov-Witten和DT理论。对于Calabi-Yau三折叠,后一等价性应被视为导出范畴中的一个穿墙公式。对新的不变量进行了几次计算。在Fano情形下,发现了非奇异嵌入曲线的局部贡献。在局部toric Calabi-Yau情形下,描述了拓扑顶点的一种全新形式。对的虚拟枚举与Gopakumar和VAFA的BPS状态计数的几何关系密切。我们证明了我们对Gromov-Witten不变量的积分预言与BPS积分一致。相反,BPS几何在对的枚举上施加了很强的条件。
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英文标题:
《Curve counting via stable pairs in the derived category》
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作者:
R. Pandharipande and R. P. Thomas
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最新提交年份:
2019
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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:Physics 物理学
二级分类:High Energy Physics - Theory 高能物理-理论
分类描述:Formal aspects of quantum field theory. String theory, supersymmetry and supergravity.
量子场论的形式方面。弦理论,超对称性和超引力。
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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:
For a nonsingular projective 3-fold $X$, we define integer invariants virtually enumerating pairs $(C,D)$ where $C\subset X$ is an embedded curve and $D\subset C$ is a divisor. A virtual class is constructed on the associated moduli space by viewing a pair as an object in the derived category of $X$. The resulting invariants are conjecturally equivalent, after universal transformations, to both the Gromov-Witten and DT theories of $X$. For Calabi-Yau 3-folds, the latter equivalence should be viewed as a wall-crossing formula in the derived category. Several calculations of the new invariants are carried out. In the Fano case, the local contributions of nonsingular embedded curves are found. In the local toric Calabi-Yau case, a completely new form of the topological vertex is described. The virtual enumeration of pairs is closely related to the geometry underlying the BPS state counts of Gopakumar and Vafa. We prove that our integrality predictions for Gromov-Witten invariants agree with the BPS integrality. Conversely, the BPS geometry imposes strong conditions on the enumeration of pairs.
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PDF链接:
https://arxiv.org/pdf/0707.2348