Unique ergodicity for foliations in ℙ^2 with an invariant curve

Inventiones mathematicae(2017)

引用 0|浏览0
暂无评分
摘要
Consider a foliation in the projective plane admitting a projective line as the unique invariant algebraic curve. Assume that the foliation is generic in the sense that its singular points are hyperbolic. We show that there is a unique positive dd^c -closed (1, 1)-current of mass 1 which is directed by the foliation and this is the current of integration on the invariant line. A unique ergodicity theorem for the distribution of leaves follows: for any leaf L , appropriate averages of L converge to the current of integration on the invariant line. The result uses an extension of our theory of densities for currents. Foliations on compact Kähler surface with one or more invariant curves are also considered.
更多
查看译文
关键词
37F75,37A
AI 理解论文
溯源树
样例
生成溯源树,研究论文发展脉络
Chat Paper
正在生成论文摘要