# On certain duality of N\'eron-Severi lattices of supersingular K3 surfaces

@article{Kond2012OnCD, title={On certain duality of N\'eron-Severi lattices of supersingular K3 surfaces}, author={Shigeyuki Kondō and Ichiro Shimada}, journal={arXiv: Algebraic Geometry}, year={2012} }

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 N\'eron-Severi 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… Expand

#### 11 Citations

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We show that supersingular K3 surfaces in characteristic $$p\ge 5$$p≥5 are related by purely inseparable isogenies. This implies that they are unirational, which proves conjectures of Artin, Rudakov,… Expand