{"title":"相对Gromov-Witten和最大接触二次曲线","authors":"Giosuè Muratore","doi":"10.1007/s00013-025-02169-z","DOIUrl":null,"url":null,"abstract":"<div><p>We discuss some properties of the relative Gromov–Witten invariants counting rational curves with maximal contact order at one point. We compute the number of Cayley’s sextactic conics to any smooth plane curve. In particular, we compute the contribution, from double covers of inflectional lines, to a certain degree two relative Gromov–Witten invariant relative to the curve.</p></div>","PeriodicalId":8346,"journal":{"name":"Archiv der Mathematik","volume":"125 5","pages":"491 - 503"},"PeriodicalIF":0.5000,"publicationDate":"2025-08-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Relative Gromov–Witten and maximal contact conics\",\"authors\":\"Giosuè Muratore\",\"doi\":\"10.1007/s00013-025-02169-z\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><p>We discuss some properties of the relative Gromov–Witten invariants counting rational curves with maximal contact order at one point. We compute the number of Cayley’s sextactic conics to any smooth plane curve. In particular, we compute the contribution, from double covers of inflectional lines, to a certain degree two relative Gromov–Witten invariant relative to the curve.</p></div>\",\"PeriodicalId\":8346,\"journal\":{\"name\":\"Archiv der Mathematik\",\"volume\":\"125 5\",\"pages\":\"491 - 503\"},\"PeriodicalIF\":0.5000,\"publicationDate\":\"2025-08-16\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Archiv der Mathematik\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://link.springer.com/article/10.1007/s00013-025-02169-z\",\"RegionNum\":4,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q3\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Archiv der Mathematik","FirstCategoryId":"100","ListUrlMain":"https://link.springer.com/article/10.1007/s00013-025-02169-z","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"MATHEMATICS","Score":null,"Total":0}
We discuss some properties of the relative Gromov–Witten invariants counting rational curves with maximal contact order at one point. We compute the number of Cayley’s sextactic conics to any smooth plane curve. In particular, we compute the contribution, from double covers of inflectional lines, to a certain degree two relative Gromov–Witten invariant relative to the curve.
期刊介绍:
Archiv der Mathematik (AdM) publishes short high quality research papers in every area of mathematics which are not overly technical in nature and addressed to a broad readership.