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摘要翻译：
我们确定了与A_n型奇点有关的表面分辨率点的Hilbert格式的等变量子上同调的两点不变量。编码这些不变量的算子用仿射李代数\HAT{gl}(n+1)对其基本表示的作用来表示。假设一定的非简并猜想，这些算子决定了量子上同调环的全结构。证明了A_n×P^1的量子上同调与Gromov-Witten/Donaldson-Thomas理论之间的关系。最后，我们讨论了相关的量子微分方程的单群性质，并对D型和E型奇点进行了推广。
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英文标题：
《Quantum cohomology of the Hilbert scheme of points on A_n-resolutions》
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作者：
D. Maulik, A. Oblomkov
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最新提交年份：
2009
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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：Representation Theory 表象理论
分类描述：Linear representations of algebras and groups, Lie theory, associative algebras, multilinear algebra
代数和群的线性表示，李理论，结合代数，多重线性代数
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英文摘要：
We determine the two-point invariants of the equivariant quantum cohomology of the Hilbert scheme of points of surface resolutions associated to type A_n singularities. The operators encoding these invariants are expressed in terms of the action of the affine Lie algebra \hat{gl}(n+1) on its basic representation. Assuming a certain nondegeneracy conjecture, these operators determine the full structure of the quantum cohomology ring. A relationship is proven between the quantum cohomology and Gromov-Witten/Donaldson-Thomas theories of A_n x P^1. We close with a discussion of the monodromy properties of the associated quantum differential equation and a generalization to singularities of type D and E.
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PDF链接：
https://arxiv.org/pdf/0802.2737
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