Details
| Original language | English |
|---|---|
| Article number | 106558 |
| Number of pages | 17 |
| Journal | Journal of Pure and Applied Algebra |
| Volume | 225 |
| Issue number | 4 |
| Early online date | 8 Sept 2020 |
| Publication status | Published - Apr 2021 |
Abstract
Keywords
- math.AG, K3 surface, Automorphism, Abelian surface, Supersingular, Cusp
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In: Journal of Pure and Applied Algebra, Vol. 225, No. 4, 106558, 04.2021.
Research output: Contribution to journal › Article › Research › peer review
}
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 -