Algebraic Surfaces of General Type with Small c_1^2 in Positive Characteristic

Details Algebraic Surfaces of General Type with Small c_1^2 in Positive Characteristic Algebraic Surfaces of General Type with Small c_1^2 in Positive Characteristic

2007-02-19

arxiv.org/abs/math/0702548v2

Nagoya Math. J. 191, 111-134 (2008)

Mathematics

Algebraic Geometry

15 pages, minor corrections

Scientific paper

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.

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