Shafarevich maps and plurigenera of algebraic varieties.
A Steiner bundle on has a linear resolution of the form . In this paper we prove that a generic Steiner bundle is simple if and only if is less or equal to 1. In particular we show that either is exceptional or it satisfies the inequality .
We study local properties of quasi-unipotent overconvergent -isocrystals on a curve over a perfect field of positive characteristic . For a --module over the Robba ring , we define the slope filtration for Frobenius structures. We prove that an overconvergent -isocrystal is quasi-unipotent if and only if it has the slope filtration for Frobenius structures locally at every point on the complement of the curve.