Some Topics in Several Complex Variables

Projective embedding of log Riemann surfaces and K-stability

914(星期四), 15:30 - 17:30

数学院南楼N913

Given a smooth polarized Riemann surface  endowed with a hyperbolic metric with cusp singularities along a divisor D, we show the  projective embedding of  defined by  is asymptotically almost balanced in a weighted sense. The proof depends on sufficiently precise understanding of the behavior of the Bergman kernel in three regions, with the most crucial one being the neck region around . This is the first step towards understanding the algebro-geometric stability of extremal Kähler metrics with singularities.

This is a joint work with Song Sun.