Seminar: Takayuki Koike (G.15.25)
In Nemirovski's proof of the nonexistence theorem for two-dimensional Stein domains with compact Levi-flat boundaries admitting plurisubharmonic defining functions, he introduced and studied a function defined by integrating a suitable form over each level set of the defining function. Related techniques were later employed by Fu and Shaw in their study of the Diederich-Fornaess exponent.
In this talk, I will present an application of such pluripotential arguments to the study of semi-positive holomorphic line bundles on (compact) Kahler manifolds. In particular, I will discuss a characterization of semi-positivity for effective divisors of numerical dimension one in terms of the existence of certain pseudoflat systems of neighborhoods of their supports, and its connection with the Hartogs extension phenomenon.
