Algebraic Geometry Seminar
Gordon HEIER
University of Houston
Reduction of manifolds with semi-negative holomorphic sectional curvature
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.
Wednesday November 29, 2017 at 4:00 PM in SEO 427