Algebraic Surfaces of General Type with Small c 2 1 in Positive Characteristic

By C. Liedtke. Nagoya mathematical journal, 2007

79 citations recorded by the source corpus.

Abstract We establish Noether’s inequality for surfaces of general type in positive characteristic. Then we extend Enriques’ and Horikawa’s classification of surfaces on the Noether line, the so-called Horikawa surfaces. We construct examples for all possible numerical invariants and in arbitrary characteristic, where we need foliations and deformation techniques to handle characteristic 2. Finally, we show that Horikawa surfaces lift to characteristic zero.

Subfields: Applied Mathematics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/b5ee74d64c330b29eef4b517e0daf9ae56c4ee61