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
  • [21] Classification of Toric log Del Pezzo Surfaces having Picard Number 1 and Index ≤ 3
    Dimitrios I. Dais
    Results in Mathematics, 2009, 54 : 219 - 252
  • [22] On log del Pezzo surfaces in large characteristic
    Cascini, Paolo
    Tanaka, Hiromu
    Witaszek, Jakub
    COMPOSITIO MATHEMATICA, 2017, 153 (04) : 820 - 850
  • [23] Automorphisms of del Pezzo surfaces in odd characteristic
    Dolgachev, Igor
    Martin, Gebhard
    JOURNAL OF THE LONDON MATHEMATICAL SOCIETY-SECOND SERIES, 2024, 109 (05):
  • [24] Classification of Toric log Del Pezzo Surfaces having Picard Number 1 and Index ≤ 3
    Dais, Dimitrios I.
    RESULTS IN MATHEMATICS, 2009, 54 (3-4) : 219 - 252
  • [25] Classification of rank two weak Fano bundles on del Pezzo threefolds of degree four
    Takeru Fukuoka
    Wahei Hara
    Daizo Ishikawa
    Mathematische Zeitschrift, 2022, 301 : 2883 - 2905
  • [26] Classification of rank two weak Fano bundles on del Pezzo threefolds of degree four
    Fukuoka, Takeru
    Hara, Wahei
    Ishikawa, Daizo
    MATHEMATISCHE ZEITSCHRIFT, 2022, 301 (03) : 2883 - 2905
  • [27] Bounds for del pezzo surfaces of degree two
    Ghosh, Aritra
    Kumar, Sumit
    Mallesham, Kummari
    Singh, Saurabh Kumar
    QUARTERLY JOURNAL OF MATHEMATICS, 2023, 74 (01): : 247 - 271
  • [28] Classification of exceptional log del Pezzo surfaces with δ=1
    Kudryavtsev, SA
    IZVESTIYA MATHEMATICS, 2003, 67 (03) : 461 - 497
  • [29] On the combinatorial classification of toric log del Pezzo surfaces
    Kasprzyk, Alexander M.
    Kreuzer, Maximilian
    Nill, Benjamin
    LMS JOURNAL OF COMPUTATION AND MATHEMATICS, 2010, 13 : 33 - 46
  • [30] K3 surfaces of Picard rank one and degree two
    Elsenhans, Andreas-Stephan
    Jahnel, Joerg
    ALGORITHMIC NUMBER THEORY, 2008, 5011 : 212 - 225
12345