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Toshiyuki Katsura

Publications and source records attributed to Toshiyuki Katsura.

24 records · Page 2Linked to original sources
arXiv2014

A 1-dimensional family of Enriques surfaces in characteristic 2 covered by the supersingular K3 surface with Artin invariant 1

We give a 1-dimensional family of classical and supersingular Enriques surfaces in characteristic 2 covered by the supersingular K3 surface with Artin invariant 1. Moreover we show that there exist 30 nonsingular rational curves and ten non-effective (-2)-divisors on these Enriques surfaces whose reflection group is of finite index in the orthogonal group of the Neron-Severi lattice modulo torsion.

math.AG↗
arXiv2014

On the supersingular K3 surface in characteristic 5 with Artin invariant 1

We present three interesting projective models of the supersingular K3 surface X in characteristic 5 with Artin invariant 1. For each projective model, we determine smooth rational curves on X with the minimal degree and the projective automorphism group. Moreover, by using the superspecial abelian surface, we construct six sets of 16 disjoint smooth rational curves on X, and show that they form a beautiful configuration.

math.AG↗
arXiv2011

Rational curves on the supersingular K3 surface with Artin invariant 1 in characteristic 3

We show the existence of 112 non-singular rational curves on the supersingular K3 surface with Artin invariant 1 in characteristic 3 by several ways. Using these rational curves, we have a $(16)_{10}$-configuration and a $(280_{4}, 112_{10})$-configuration on the K3 surface. Moreover we study the Picard lattice by using the theory of the Leech lattice. The 112 non-singular rational curves correspond to 112 Leech roots.

math.AG↗
arXiv2011

A note on a supersingular K3 surface in characteristic 2

We construct, on a supersingular K3 surface with Artin invariant 1 in characteristic 2, a set of 21 disjoint smooth rational curves and another set of 21 disjoint smooth rational curves such that each curve in one set intersects exactly 5 curves from the other set with multiplicity 1 by using the structure of a generalized Kummer surface.

math.AG↗