On certain duality of NéronSeveri lattices of supersingular K3 surfaces
Abstract
Let X and Y be supersingular K3 surfaces defined over an algebraically closed field. Suppose that the sum of their Artin invariants is 11. Then there exists a certain duality between their NéronSeveri lattices. We investigate geometric consequences of this duality. As an application, we classify genus one fibrations on supersingular K3 surfaces with Artin invariant 10 in characteristic 2 and 3, and give a set of generators of the automorphism group of the nef cone of these supersingular K3 surfaces. The difference between the automorphism group of a supersingular K3 surface X and the automorphism group of its nef cone is determined by the period of X. We define the notion of genericity for supersingular K3 surfaces in terms of the period, and prove the existence of generic supersingular K3 surfaces in odd characteristics for each Artin invariant larger than 1.
 Publication:

arXiv eprints
 Pub Date:
 December 2012
 arXiv:
 arXiv:1212.0269
 Bibcode:
 2012arXiv1212.0269K
 Keywords:

 Mathematics  Algebraic Geometry;
 14J28
 EPrint:
 23 pages. Title is shortened. Some details are omitted