Mixed Frobenius Structure and Local Quantum Cohomology
Mixed Frobenius Structure and Local Quantum Cohomology
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DOI：
10.4171/prims/173
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发表时间：
2014-05
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影响因子：
--
通讯作者：
Y. Konishi;S. Minabe
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文献类型：
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作者：
Y. Konishi;S. Minabe
本文是Arxiv：1209.5550的续篇，其中引入了混合Frobenius结构的概念，作为Frobenius流形结构的推广。粗略地说，MFS的定义是将Frobenius流形的度量替换为配备了关于其分次商的度量的切丛上的滤子。本文的目的是在光滑射影簇的上同调上构造一个MFS，该簇的乘积是由凹向量丛扭曲的量子积的非等变极限。我们证明了在等变的情况下，这样的MFS是作为Frobenius结构的非等变极限而自然得到的。
This paper is a sequel to arXiv:1209.5550 where the notion of mixed Frobenius structure (MFS) was introduced as a generalization of the structure of a Frobenius manifold. Roughly speaking, the MFS is defined by replacing a metric of the Frobenius manifold with a filtration on the tangent bundle equipped with metrics on its graded quotients. The purpose of the current paper is to construct a MFS on the cohomology of a smooth projective variety whose multiplication is the non-equivariant limit of the quantum product twisted by a concave vector bundle. We show that such a MFS is naturally obtained as the non-equivariant limit of the Frobenius structure in the equivariant setting.