Uniruled Surfaces of General Type

Abstract

We give a systematic construction of uniruled surfaces in positive characteristic. Using this construction, we find surfaces of general type with non-trivial vector fields, surfaces with arbitrarily non-reduced Picard schemes as well as surfaces with inseparable canonical maps. In particular, we show that some previously known pathologies are not sporadic but exist in abundance.

21 pages, some mistakes corrected and new pathologies !