Abstract
We show that all extremal elliptic surfaces in characteristic 2 and 3 are obtained from rational extremal elliptic surfaces as purely inseparable base extensions. As a corollary, we can show that the automorphism group of every supersingular elliptic $K3$ surface has an element of infinite order which acts trivially on the global sections of the sheaf of differential forms of degree 2. We also determine the structures of Mordell- Weil groups for extremal rational elliptic surfaces in these characteristics.
Citation
Hiroyuki Ito. "On extremal elliptic surfaces in characteristic 2 and 3." Hiroshima Math. J. 32 (2) 179 - 188, July 2002. https://doi.org/10.32917/hmj/1151007555
Information