Stable maps and stable quotients
Stable maps and stable quotients
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稳定的映射和稳定的商
DOI：
10.1112/s0010437x14007258
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发表时间：
2013
影响因子：
1.8
通讯作者：
C. Manolache
中科院分区：
文献类型：
--
作者：
C. Manolache
摘要：我们分析了从曲线到格拉斯曼映射的模空间的两个紧缩之间的关系：稳定映射的 Kontsevich 模空间和稳定商的 Marian-Oprea-Pandharipande 模空间。我们构造了一个模空间，它支配着格拉斯曼稳定映射的模空间和稳定商的模空间，并为我们的模空间配备了虚拟基本类。我们使用虚拟前推公式将所有三个模空间的虚拟基本类联系起来。这给出了 Marian-Oprea-Pandharipande 定理的新证明：定义为稳定商模空间中的交集数的枚举不变量与 Gromov-Witten 不变量一致。
Abstract We analyze the relationship between two compactifications of the moduli space of maps from curves to a Grassmannian: the Kontsevich moduli space of stable maps and the Marian–Oprea–Pandharipande moduli space of stable quotients. We construct a moduli space which dominates both the moduli space of stable maps to a Grassmannian and the moduli space of stable quotients, and equip our moduli space with a virtual fundamental class. We relate the virtual fundamental classes of all three moduli spaces using the virtual push-forward formula. This gives a new proof of a theorem of Marian–Oprea–Pandharipande: that enumerative invariants defined as intersection numbers in the stable quotient moduli space coincide with Gromov–Witten invariants.