对于一个满足“强Lefschetz条件”的Kähler SL-G-流形（X，ω），本文在弦上同调Hk（X，G）上构造了一个Hodge结构，在素弦上同调PHk（X，ω，G）上构造了一个极化Hodge结构，然后通过弦Dolbeault上同调H*，*（X，G）在H*（X，G）上得到了一个被X上所有Kähler类所极化的混合Hodge结构.所有这些（极化混合） Hodge结构都附带一个自然的G-作用.本文证明这些（极化混合） Hodge结构的G-不变部分同构于对应的整体商Kähler SL-轨形（X=[X/G]，σ）的Chen-Ruan上同调群的（极化混合） Hodge结构，其中σ是由ω所诱导的X上的Kähler形式.
Abstract
In this paper, for a Kähler SL-G-manifold (X, ω) that satisfies a "Hard Lef-schetz Condition" we construct a Hodge structure on its Stringy cohomology Hk(X, G), a polarized Hodge structure on its primitive Stringy cohomology PHk(X, ω, G). By using the Stringy Dolbeault cohomology H*,*(X, G) we also get a mixed Hodge structure on H*(X, G) that is polarized by every Kähler class of X. All these (polarized mixed) Hodge structures admit natural G-actions. We show that the G-invariant parts of these (polarized mixed) Hodge structures are isomorphic to those (polarized mixed) Hodge structures of the Chen-Ruan cohomology group of (X=[X/G], σ), the global quotient Kähler SL-orbifold with σ induced by ω.
关键词
弦上同调 /
G-Hodge结构 /
极化混合G-Hodge结构
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Key words
stingy cohomology /
G-Hodge structure /
polarized mixed G-Hodge structure
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参考文献
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脚注
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基金
国家自然科学基金（11501393，12071322，11626050，11871126，11801048，11901069，12071050）；四川省科技计划项目（2019YJ0509）；四川师范大学Laurent数学研究中心和可视化计算与虚拟现实四川省重点实验室资助项目；重庆市教委科技研究项目（KJ1600324）；重庆市科委自然科学项目（cstc2018jcyjAX0465）
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