A hyperbolic metric and stability conditions on K3 surfaces with rho=1

摘要

We introduce a hyperbolic metric on the (normalized) space of stability conditions on projective K3 surfaces X with Picard rank rho(X) = 1 and give some applications. We show that all walls are geodesic in the normalized space with respect to the hyperbolic metric. Furthermore we demonstrate how the hyperbolic metric is helpful for us by discussing some topics. As an application of the metric, we give an explicit example of stable complexes in large volume limits.