报告题目：

Finding Rational Curves by Forgetful Maps

报 告 人：

宗润弘 博士（德国美因茨大学University of Mainz ）

报告时间：

2018年05月09日14:30--15:30

报告地点：

理学院东北楼四楼办公厅（404）

报告摘要：

In this talk, we are mainly concerned with the geometry of rational curves on algebraic varieties. Our main object of study is rationally connected varieties, a kind of varieties that contain“plenty”of rational curves. It was shown by Koll´ar-Miyaoka-Mori that a kind of“smoothing of comb”technique is available on this kind of varieties. We firstly show a most general form of this kind of“smoothing of comb”technique exists, which extends all the“smoothing of comb”techniques in the literature before. Then we apply this generalized technique to study the geometry of forgetful maps between moduli spaces of stable maps and twisted stable maps to rationally connected varieties. As a result, we solve several open questions on topology, geometry and arithmetic of rationally connected varieties.