论文标题
在整体仿射流形和完美配对上的热带周期的同源理论
A homology theory for tropical cycles on integral affine manifolds and a perfect pairing
论文作者
论文摘要
我们介绍了与奇异性积分仿射歧管上的热带周期的同源性和同源性的CAP产品配对。我们表明，当多种多样的奇异奇异之处时，第一级的配对在第一级上是完美的。通过与Siebert的联合合作，配对计算时期积分及其完美性意味着规范的Calabi-yau变性的历史性。我们还为Strominger-Yau-Zaslow纤维化提供了一个交集理论应用。通过简单方法处理可构造式滑轮的帽子产品和庞加莱 - 莱夫斯兹的处理可能具有独立的关注。
We introduce a cap product pairing for homology and cohomology of tropical cycles on integral affine manifolds with singularities. We show the pairing is perfect over $\mathbb{Q}$ in degree one when the manifold has at worst symple singularities. By joint work with Siebert, the pairing computes period integrals and its perfectness implies the versality of canonical Calabi-Yau degenerations. We also give an intersection theoretic application for Strominger-Yau-Zaslow fibrations. The treatment of the cap product and Poincaré-Lefschetz by simplicial methods for constructible sheaves might be of independent interest.
