The 2-divisibility of divisors on K3 surfaces in characteristic 2

IF 0.8 3区数学 Q2 MATHEMATICS

Mathematische Nachrichten Pub Date : 2025-05-28 DOI:10.1002/mana.12024

Toshiyuki Katsura, Shigeyuki Kondō, Matthias Schütt

{"title":"The 2-divisibility of divisors on K3 surfaces in characteristic 2","authors":"Toshiyuki Katsura, Shigeyuki Kondō, Matthias Schütt","doi":"10.1002/mana.12024","DOIUrl":null,"url":null,"abstract":"We show that K3 surfaces in characteristic 2 can admit sets of <math>\n <semantics>\n <mi>n</mi>\n <annotation>$n$</annotation>\n </semantics></math> disjoint smooth rational curves whose sum is divisible by 2 in the Picard group, for each <math>\n <semantics>\n <mrow>\n <mi>n</mi>\n <mo>=</mo>\n <mn>8</mn>\n <mo>,</mo>\n <mn>12</mn>\n <mo>,</mo>\n <mn>16</mn>\n <mo>,</mo>\n <mn>20</mn>\n </mrow>\n <annotation>$n=8,12,16,20$</annotation>\n </semantics></math>. More precisely, all values occur on supersingular K3 surfaces, with exceptions only at Artin invariants 1 and 10, while on K3 surfaces of finite height, only <math>\n <semantics>\n <mrow>\n <mi>n</mi>\n <mo>=</mo>\n <mn>8</mn>\n </mrow>\n <annotation>$n=8$</annotation>\n </semantics></math> is possible.","PeriodicalId":49853,"journal":{"name":"Mathematische Nachrichten","volume":"298 6","pages":"1964-1988"},"PeriodicalIF":0.8000,"publicationDate":"2025-05-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1002/mana.12024","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Mathematische Nachrichten","FirstCategoryId":"100","ListUrlMain":"https://onlinelibrary.wiley.com/doi/10.1002/mana.12024","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS","Score":null,"Total":0}

引用次数: 0

Abstract

We show that K3 surfaces in characteristic 2 can admit sets of $n$ disjoint smooth rational curves whose sum is divisible by 2 in the Picard group, for each $n = 8, 12, 16, 20$ . More precisely, all values occur on supersingular K3 surfaces, with exceptions only at Artin invariants 1 and 10, while on K3 surfaces of finite height, only $n = 8$ is possible.

查看原文本刊更多论文

特征2的K3曲面上因子的2可除性

我们证明了特征2中的K3曲面可以容纳n$ n$不相交的光滑有理曲线集合，其和在Picard群中可被2整除，对于每个n = 8,12,16，20$ n=8,12,16,20$。更准确地说，所有的值都出现在超奇异的K3曲面上，只有在Artin不变量1和10处例外，而在有限高度的K3曲面上，只有n=8$ n=8$是可能的。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

求助全文

约1分钟内获得全文求助全文

来源期刊

Mathematische Nachrichten 数学-数学

CiteScore

1.50

自引率

0.00%

发文量

157

审稿时长

4-8 weeks

期刊介绍： Mathematische Nachrichten - Mathematical News publishes original papers on new results and methods that hold prospect for substantial progress in mathematics and its applications. All branches of analysis, algebra, number theory, geometry and topology, flow mechanics and theoretical aspects of stochastics are given special emphasis. Mathematische Nachrichten is indexed/abstracted in Current Contents/Physical, Chemical and Earth Sciences; Mathematical Review; Zentralblatt für Mathematik; Math Database on STN International, INSPEC; Science Citation Index