TY - JOUR

T1 - K3 surfaces with 9 cusps in characteristic p

AU - Katsura, Toshiyuki

AU - Schütt, Matthias

N1 - Funding information: Partially supported by JSPS Grant-in-Aid for Scientific Research (B) No. 15H03614.

PY - 2021/4

Y1 - 2021/4

N2 - We study K3 surfaces with 9 cusps, i.e. 9 disjoint A 2 configurations of smooth rational curves, over algebraically closed fields of characteristic p≠3. Much like in the complex situation studied by Barth, we prove that each such surface admits a triple covering by an abelian surface. Conversely, we determine which abelian surfaces with order three automorphisms give rise to K3 surfaces. We also investigate how K3 surfaces with 9 cusps hit the supersingular locus.

AB - We study K3 surfaces with 9 cusps, i.e. 9 disjoint A 2 configurations of smooth rational curves, over algebraically closed fields of characteristic p≠3. Much like in the complex situation studied by Barth, we prove that each such surface admits a triple covering by an abelian surface. Conversely, we determine which abelian surfaces with order three automorphisms give rise to K3 surfaces. We also investigate how K3 surfaces with 9 cusps hit the supersingular locus.

KW - math.AG

KW - K3 surface

KW - Automorphism

KW - Abelian surface

KW - Supersingular

KW - Cusp

UR - http://www.scopus.com/inward/record.url?scp=85091033522&partnerID=8YFLogxK

U2 - 10.1016/j.jpaa.2020.106558

DO - 10.1016/j.jpaa.2020.106558

M3 - Article

VL - 225

JO - Journal of Pure and Applied Algebra

JF - Journal of Pure and Applied Algebra

SN - 0022-4049

IS - 4

M1 - 106558

ER -