Hiroshima Mathematical Journal

On extremal elliptic surfaces in characteristic 2 and 3

Hiroyuki Ito

Full-text: Open access

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.

Article information

Source
Hiroshima Math. J., Volume 32, Number 2 (2002), 179-188.

Dates
First available in Project Euclid: 22 June 2006

Permanent link to this document
https://projecteuclid.org/euclid.hmj/1151007555

Digital Object Identifier
doi:10.32917/hmj/1151007555

Mathematical Reviews number (MathSciNet)
MR1925896

Zentralblatt MATH identifier
1050.14026

Subjects
Primary: 14J27: Elliptic surfaces
Secondary: 11G05: Elliptic curves over global fields [See also 14H52] 14J28: $K3$ surfaces and Enriques surfaces

Citation

Ito, Hiroyuki. On extremal elliptic surfaces in characteristic 2 and 3. Hiroshima Math. J. 32 (2002), no. 2, 179--188. doi:10.32917/hmj/1151007555. https://projecteuclid.org/euclid.hmj/1151007555


Export citation