scholarly journals A note on a supersingular K3 surface in characteristic 2

2012 ◽  
pp. 243-255
Author(s):  
Toshiyuki Katsura ◽  
Shigeyuki Kondō
Keyword(s):  
K3 Surface ◽  
Characteristic 2 ◽  
Supersingular K3 Surface

scholarly journals Two algebraic deformations of a K3 surface

1981 ◽  
Vol 82 ◽  
pp. 1-26
Author(s):  
Daniel Comenetz
Keyword(s):  
Hyperelliptic Curve ◽  
Double Cover ◽  
Rational Curves ◽  
K3 Surface ◽  
Quartic Surface ◽  
Quadric Cone ◽  
Birational Model ◽  
Affine Line ◽  
Characteristic 2 ◽  
General Member

Let X be a nonsingular algebraic K3 surface carrying a nonsingular hyperelliptic curve of genus 3 and no rational curves. Our purpose is to study two algebraic deformations of X, viz. one specialization and one generalization. We assume the characteristic ≠ 2. The generalization of X is a nonsingular quartic surface Q in P3 : we wish to show in § 1 that there is an irreducible algebraic family of surfaces over the affine line, in which X is a member and in which Q is a general member. The specialization of X is a surface Y having a birational model which is a ramified double cover of a quadric cone in P3.

scholarly journals DYNAMICS ON SUPERSINGULAR K3 SURFACES AND AUTOMORPHISMS OF SALEM DEGREE 22

2016 ◽  
Vol 227 ◽  
pp. 1-15
Author(s):  
SIMON BRANDHORST
Keyword(s):  
Characteristic Zero ◽  
K3 Surfaces ◽  
K3 Surface ◽  
Supersingular K3 Surface

In this paper, we exhibit explicit automorphisms of maximal Salem degree 22 on the supersingular K3 surface of Artin invariant one for all primes $p\equiv 3~\text{mod}\,4$ in a systematic way. Automorphisms of Salem degree 22 do not lift to any characteristic zero model.

scholarly journals On the Supersingular $K3$ Surface in Characteristic $5$ with Artin Invariant $1$

2014 ◽  
Vol 63 (4) ◽  
pp. 803-844 ◽  
Author(s):  
Toshiyuki Katsura ◽  
Shigeyuki Kondo ◽  
Ichiro Shimada
Keyword(s):  
K3 Surface ◽  
Supersingular K3 Surface
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