The Poincaré problem for a foliated surface

：吕鑫（华东师范大学）
：2024-12-05 09:30
：海韵园实验楼S204

报告人：吕鑫（华东师范大学）

时  间：2024年12月5日9:30

地  点：海韵园实验楼S204

内容摘要:

Let F be a foliation on a smooth projective surface S over the complex numbers. We introduce three birational non-negative invariants c_1^2(F), c_2(F) and chi(F), called the Chern numbers. If the foliation F is not of general type, the first Chern number c_1^2(F)=0, and c_2(F)=chi(F)=0 except when F is induced by a non-isotrivial fibration of genus g=1. If F is of general type, we obtain a slope inequality when F is algebraically integrable. As a corollary, F is always transcendental if the slope is less than 2. On the other hand, we also prove three sharp Noether type inequalities if F is of general type. As applications, we obtain a criterion for foliations to be transcendental using Noether type inequalities, and we also give a partial positive answer to the question on the lower bound on the volume of a foliation of general type. This is a joint work with Professor Shengli Tan.

个人简介：

吕鑫，华东师范大学教授。2013年博士毕业于华东师范大学，之后在德国美因茨大学从事博士后研究。吕鑫教授的研究领域为代数几何，研究兴趣包括代数曲线的模空间、代数曲面理论，叶层化等，论文发表在 Ann. Sci. Éc. Norm. Supér., J. Math. Pures Appl., Adv. Math. , Compos. Math., Trans. Amer. Math. Soc. 等期刊。

 

联系人：刘文飞