光滑del Pezzo对数Calabi-Yau对的 Tropical对应
代数几何
2022-05-06 v4
摘要
考虑一个由次数的光滑del Pezzo曲面与一条光滑反正则除子构成的对数Calabi-Yau对。我们证明了的零亏格对数Gromov-Witten不变量(与在一点以最大切触相交)与由Gross-Siebert重构算法得到的的对偶相交复形中出现的相容墙结构之间的对应。更确切地说,相容墙结构中附着于无界墙的函数之乘积的对数给出了这些不变量的生成函数。
引用
@article{arxiv.2005.14018,
title = {Tropical correspondence for smooth del Pezzo log Calabi-Yau pairs},
author = {Tim Graefnitz},
journal= {arXiv preprint arXiv:2005.14018},
year = {2022}
}
备注
74 pages; v4: added {\S}7 on higher genus; a shortened version of this paper will appear in Journal of Algebraic Geometry