Quantum differential systems and construction of rational structures
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- 作者：Antoine Douai
- 关键词：32S40 ; 14J33 ; 34M35
- 刊名：manuscripta mathematica
- 出版年：2014
- 出版时间：November 2014
- 年：2014
- 卷：145
- 期：3-4
- 页码：285-317
- 全文大小：385 KB
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1. Laboratoire J.A Dieudonné, UMR CNRS 7351, Université de Nice, Parc Valrose, 06108, Nice Cedex 2, France - ISSN：1432-1785
文摘
We consider mirror symmetry (A-side vs B-side, namely singularity side) in the framework of quantum differential systems. We focuse on the logarithmic non-resonant case, which describes the geometric situation and we show that such systems provide a good framework in order to generalize the construction of the rational structure given by Katzarkov, Kontsevich and Pantev for the complex projective space. As an application, we give a closed formula for the rational structure defined by the Lefschetz thimbles on the flat sections of the Gauss-Manin connection associated with the Landau–Ginzburg models of weighted projective spaces (a class of Laurent polynomials). As a by-product, using a mirror theorem, we get a rational structure on the orbifold cohomology of weighted projective spaces. The formula on the B-side is more complicated than the one on the A-side (the latter agrees with one of Iritani’s results), depending on numerous combinatorial data which are rearranged after the mirror transformation.