Classification of Du Val del Pezzo surfaces of Picard rank one in characteristic two and three

被引：1
|
作者：
Kawakami, Tatsuro [1 ]
Nagaoka, Masaru [2 ]
机构：
[1] Kyoto Univ, Grad Sch Sci, Dept Math, Kyoto 6068502, Japan
[2] Gakushuin Univ, 1-5-1 Mejiro,Toshima Ku, Tokyo 1718588, Japan
来源：
JOURNAL OF ALGEBRA | 2023年 / 636卷
关键词：
Del Pezzo surfaces; Frobenius splitting; Positive characteristic; RATIONAL ELLIPTIC-SURFACES; MORDELL-WEIL GROUPS; CHARACTERISTIC-P;
D O I：
10.1016/j.jalgebra.2023.08.027
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
In this paper, we classify Du Val del Pezzo surfaces of Picard rank one in characteristic two and three. We also show that if a Du Val del Pezzo surface is Frobenius split, then a general anti-canonical member is smooth. Furthermore, in characteristic two, it is an ordinary elliptic curve.(c) 2023 Elsevier Inc. All rights reserved.
引用
收藏
页码：603 / 625
页数：23
相关论文
共 50 条
  • [31] MIRROR SYMMETRY AND THE CLASSIFICATION OF ORBIFOLD DEL PEZZO SURFACES
    Akhtar, Mohammad
    Coates, Tom
    Corti, Alessio
    Heuberger, Liana
    Kasprzyk, Alexander
    Oneto, Alessandro
    Petracci, Andrea
    Prince, Thomas
    Tveiten, Ketil
    PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 2016, 144 (02) : 513 - 527
  • [32] DEL PEZZO SURFACES AND MORI FIBER SPACES IN POSITIVE CHARACTERISTIC
    Fanelli, Andrea
    Schroeer, Stefan
    TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 2020, 373 (03) : 1775 - 1843
  • [33] Log canonical thresholds of del Pezzo surfaces in characteristic p
    Martinez-Garcia, Jesus
    MANUSCRIPTA MATHEMATICA, 2014, 145 (1-2) : 89 - 110
  • [34] Log canonical thresholds of del Pezzo surfaces in characteristic p
    Jesus Martinez-Garcia
    Manuscripta Mathematica, 2014, 145 : 89 - 110
  • [35] CONCURRENT LINES ON DEL PEZZO SURFACES OF DEGREE ONE
    Van Luijk, Ronald
    Winter, Rosa
    MATHEMATICS OF COMPUTATION, 2022, 92 (339) : 451 - 481
  • [36] Compact moduli of degree one del Pezzo surfaces
    Kenneth Ascher
    Dori Bejleri
    Mathematische Annalen, 2022, 384 : 1 - 31
  • [37] Cox rings of degree one del Pezzo surfaces
    Testa, Damiano
    Varilly-Alvarado, Anthony
    Velasco, Mauricio
    ALGEBRA & NUMBER THEORY, 2009, 3 (07) : 729 - 761
  • [38] Toric log del Pezzo surfaces with one singularity
    Dais, Dimitrios I.
    ADVANCES IN GEOMETRY, 2020, 20 (01) : 121 - 138
  • [39] Compact moduli of degree one del Pezzo surfaces
    Ascher, Kenneth
    Bejleri, Dori
    MATHEMATISCHE ANNALEN, 2022, 384 (1-2) : 881 - 911
  • [40] Classification of singular del Pezzo surfaces over finite fields
    Blache, Regis
    Hallouin, Emmanuel
    MATHEMATISCHE ZEITSCHRIFT, 2023, 305 (04)
12345