Semi-classical Bergman kernel asymptotics on complex manifolds with boundary

讲座时间 Datetime:2022年9月7日，星期三，9:00-10:00

地点 Venue: 腾讯线上会议：875-268-136

主持人 Host：邵国宽

报告人 Speaker: 李小山

单位 Affiliation: 武汉大学

报告摘要 Abstract:

Let $M\Subset M'$ be a relatively compact complex manifold with smooth boundary and let  $L$ be a positive line bundle over $M$. Suppose that $M$ admits a holomorphic $\mathbb R$-action and the $\mathbb R$-action can be lifted to $L$. In this talk, we show that the Bergman kernel admits an asymptotic expansion with respect to a high power of $L$ under some condition involving of the curvature of the $L$ and the Levi-form of $\partial M$. As an application, we show  $L$ is big on some class of pseudoconcave manifold. This is a joint work with Chin-Yu Hsiao and George Marinescu.