Abstract

In this talk, I will report on some joint works with J.-M. Hwang on the construction of certain singular potential functions on Hermitian symmetric spaces (mostly) of non-compact type, and discuss their applications to bounding Seshadri constants of the canonical bundles on their compact quotients and bounding volumes of their complex analytic subvarieties.

In the case of complex space forms of constant (negative, zero or positive) holomorphic sectional curvature, the lower bound on the volumes of their complex analytic subvarieties thus obtained are sharp.