Miyaoka-Yau-type inequalities for Kahler-Einstein manifolds

摘要

We investigate Chern number inequalities on Kdhler-Einstein manifolds and their relations to uniformization. For Kdhler-Einstein manifolds with c(1) > 0, we prove certain Chern number inequalities in the toric case. For Kdhler-Einstein manifolds with c(1) < 0, we propose a series of Chern number inequalities, interpolating Yau's and Miyaoka's inequalities.