Gordon HEIER : Reduction of manifolds with semi-negative holomorphic sectional curvature

Posted by Mihai Paun , part of the Algebraic Geometry Seminar.

At

Nov. 29, 2017, 4 p.m.

In

SEO 427

Abstract

The interplay of various notions of hyperbolicity and the geometry and structure of a projective manifold is an important topic in complex geometry. In this spirit, we investigate a projective Kaehler manifold $M$ of semi-negative holomorphic sectional curvature $H$. We will begin with an overview of the recent progress on this topic. We will then introduce a new differential geometric numerical rank invariant which measures the number of linearly independent truly flat directions of $H$ in the tangent spaces. This invariant turns out to be bounded above by the nef dimension and bounded below by the numerical Kodaira dimension of $M$. We will also discuss a splitting theorem for $M$ in terms of the nef dimension and, under some additional hypotheses, in terms of the new rank invariant. This is joint work with S. Lu, B. Wong and F. Zheng.