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摘要翻译：
本文研究了Grassmannian上的三点亏格零Gromov-Witten不变量，这些Grassmannian将非极大各向同性子空间参数化为具有非退化对称或斜对称形式的向量空间中的非极大各向同性子空间的三点亏格零Gromov-Witten不变量。建立了经典上同调和小量子上同调环的Pieri规则，给出了任意Schubert类与某些特殊Schubert类乘积的组合公式。我们还用特殊的Schubert类生成元和关系给出了这些具有整数系数的环的表示。
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英文标题：
《Quantum Pieri rules for isotropic Grassmannians》
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作者：
Anders S. Buch, Andrew Kresch, and Harry Tamvakis
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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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英文摘要：
We study the three point genus zero Gromov-Witten invariants on the Grassmannians which parametrize non-maximal isotropic subspaces in a vector space equipped with a nondegenerate symmetric or skew-symmetric form. We establish Pieri rules for the classical cohomology and the small quantum cohomology ring of these varieties, which give a combinatorial formula for the product of any Schubert class with certain special Schubert classes. We also give presentations of these rings, with integer coefficients, in terms of special Schubert class generators and relations.
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PDF链接：
https://arxiv.org/pdf/0809.4966
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