Syzygies of compact complex hyperbolic manifolds

Abstract

We give a sufficient condition for the pluri-canonical bundles of a compact complex hyperbolic manifold to satisfy the property (Np) on linear syzygies in terms of the hyperbolic injectivity radius. In the process, we obtain sharp lower bounds for the volumes of one-dimensional complex analytic subvarieties in geodesic tubular neighborhoods of the Cartesian self-product of a compact complex hyperbolic manifold.