{"title":"德尔佩佐积分上有理曲线空间的不可还原性","authors":"Fumiya Okamura","doi":"10.1093/imrn/rnae080","DOIUrl":null,"url":null,"abstract":"We prove the irreducibility of the spaces of rational curves on del Pezzo manifolds of Picard rank $1$ and dimension $n \\ge 4$ by analyzing the fibers of evaluation maps. As a corollary, we prove Geometric Manin’s Conjecture in these cases.","PeriodicalId":0,"journal":{"name":"","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-04-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"The Irreducibility of the Spaces of Rational Curves on del Pezzo Manifolds\",\"authors\":\"Fumiya Okamura\",\"doi\":\"10.1093/imrn/rnae080\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We prove the irreducibility of the spaces of rational curves on del Pezzo manifolds of Picard rank $1$ and dimension $n \\\\ge 4$ by analyzing the fibers of evaluation maps. As a corollary, we prove Geometric Manin’s Conjecture in these cases.\",\"PeriodicalId\":0,\"journal\":{\"name\":\"\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.0,\"publicationDate\":\"2024-04-29\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.1093/imrn/rnae080\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1093/imrn/rnae080","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
The Irreducibility of the Spaces of Rational Curves on del Pezzo Manifolds
We prove the irreducibility of the spaces of rational curves on del Pezzo manifolds of Picard rank $1$ and dimension $n \ge 4$ by analyzing the fibers of evaluation maps. As a corollary, we prove Geometric Manin’s Conjecture in these cases.
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