log Calabi-Yau 曲面的镜像对称性 I
代数几何
2015-03-09 v3
摘要
我们给出了光滑射影曲面 Y 与反典范有理曲线圈 D 组成的对 (Y,D) 的镜像族的一种典范合成构造，该镜像族被构造为一个显式代数的谱，该代数由与 D 交于单点的 Y 上有理曲线的计数定义。在 D 可缩的情况下，该族给出了对偶尖点的平滑，从而证明了 Looijenga 1981 年的尖点猜想。
引用
@article{arxiv.1106.4977,
title = {Mirror symmetry for log Calabi-Yau surfaces I},
author = {Mark Gross and Paul Hacking and Sean Keel},
journal= {arXiv preprint arXiv:1106.4977},
year = {2015}
}
备注
144 pages, 3 figures, Second version significantly shorter, 109 pages. The first version has a lot of material (particularly in the introduction and material on cyclic quotient singularities) which does not appear in the new version. Download version 1 if this material is desired. Third and final version, small changes from Version 2, to appear in Publ. IHES