Slope inequalities and a Miyaoka-Yau type inequality

Abstract

For a minimal smooth projective surface S of general type over a field of characteristic p > 0, we prove thatAlbanese morphism of S must induces a genus two fiberation. A classification of surfaces with K 2 S = 32χ(O S ) is also given. The inequality also implies χ(O S ) > 0, which answers completely a question of Shepherd-Barron. Contents 19 4.3. Surfaces of general type with maximal slope 20 References 23