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中科院数学与系统科学研究院

数学研究所

中科院华罗庚数学重点实验室

多复变与复几何学术活动

Some Topics in Several Complex Variables

报告人Prof. Jingzhou Sun(Shantou University)

 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.

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