{"title":"四次曲面周期的分离","authors":"Pierre Lairez, Emre Can Sertöz","doi":"10.2140/ant.2023.17.1753","DOIUrl":null,"url":null,"abstract":"<p>We give a computable lower bound for the distance between two distinct periods of a given quartic surface defined over the algebraic numbers. The main ingredient is the determination of height bounds on components of the Noether–Lefschetz loci. This makes it possible to study the Diophantine properties of periods of quartic surfaces and to certify a part of the numerical computation of their Picard groups. </p>","PeriodicalId":50828,"journal":{"name":"Algebra & Number Theory","volume":"12 14","pages":""},"PeriodicalIF":0.9000,"publicationDate":"2023-09-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"1","resultStr":"{\"title\":\"Separation of periods of quartic surfaces\",\"authors\":\"Pierre Lairez, Emre Can Sertöz\",\"doi\":\"10.2140/ant.2023.17.1753\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<p>We give a computable lower bound for the distance between two distinct periods of a given quartic surface defined over the algebraic numbers. The main ingredient is the determination of height bounds on components of the Noether–Lefschetz loci. This makes it possible to study the Diophantine properties of periods of quartic surfaces and to certify a part of the numerical computation of their Picard groups. </p>\",\"PeriodicalId\":50828,\"journal\":{\"name\":\"Algebra & Number Theory\",\"volume\":\"12 14\",\"pages\":\"\"},\"PeriodicalIF\":0.9000,\"publicationDate\":\"2023-09-19\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"1\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Algebra & Number Theory\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.2140/ant.2023.17.1753\",\"RegionNum\":1,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q2\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Algebra & Number Theory","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.2140/ant.2023.17.1753","RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS","Score":null,"Total":0}
We give a computable lower bound for the distance between two distinct periods of a given quartic surface defined over the algebraic numbers. The main ingredient is the determination of height bounds on components of the Noether–Lefschetz loci. This makes it possible to study the Diophantine properties of periods of quartic surfaces and to certify a part of the numerical computation of their Picard groups.
期刊介绍：
ANT’s inclusive definition of algebra and number theory allows it to print research covering a wide range of subtopics, including algebraic and arithmetic geometry. ANT publishes high-quality articles of interest to a broad readership, at a level surpassing all but the top four or five mathematics journals. It exists in both print and electronic forms.
The policies of ANT are set by the editorial board — a group of working mathematicians — rather than by a profit-oriented company, so they will remain friendly to mathematicians'' interests. In particular, they will promote broad dissemination, easy electronic access, and permissive use of content to the greatest extent compatible with survival of the journal. All electronic content becomes free and open access 5 years after publication.
京公网安备 11010802042870号
京ICP备2023020795号-1
分享
求助内容：
应助结果提醒方式：
扫码关注我们
