Pub Date : 2021-04-01DOI: 10.4310/arkiv.2021.v59.n1.a7
Giosuè Muratore
Let $X$ be a smooth complex projective variety. Using a construction devised by Gathmann, we present a recursive formula for some of the Gromov–Witten invariants of $X$. We prove that, when $X$ is homogeneous, this formula gives the number of osculating rational curves at a general point of a general hypersurface of $X$. This generalizes the classical well known pairs of inflection (asymptotic) lines for surfaces in $mathbb{P}^3$ of Salmon, as well as Darboux’s 27 osculating conics.
{"title":"A recursive formula for osculating curves","authors":"Giosuè Muratore","doi":"10.4310/arkiv.2021.v59.n1.a7","DOIUrl":"https://doi.org/10.4310/arkiv.2021.v59.n1.a7","url":null,"abstract":"Let $X$ be a smooth complex projective variety. Using a construction devised by Gathmann, we present a recursive formula for some of the Gromov–Witten invariants of $X$. We prove that, when $X$ is homogeneous, this formula gives the number of osculating rational curves at a general point of a general hypersurface of $X$. This generalizes the classical well known pairs of inflection (asymptotic) lines for surfaces in $mathbb{P}^3$ of Salmon, as well as Darboux’s 27 osculating conics.","PeriodicalId":501438,"journal":{"name":"Arkiv för Matematik","volume":"35 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2021-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138534887","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
京公网安备 11010802042870号
京ICP备2023020795号-1
扫码关注我们
求助内容：
应助结果提醒方式：