{"title":"实三次的第一同调是由直线生成的","authors":"S. Finashin, V. Kharlamov","doi":"10.1090/conm/772/15485","DOIUrl":null,"url":null,"abstract":"We suggest a short proof of O.Benoist and O.Wittenberg theorem (arXiv:1907.10859) which states that for each real non-singular cubic hypersurface $X$ of dimension $\\ge 2$ the real lines on $X$ generate the whole group $H_1(X(\\Bbb R);\\Bbb Z/2)$.","PeriodicalId":296603,"journal":{"name":"Topology, Geometry, and Dynamics","volume":"3 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2019-11-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"3","resultStr":"{\"title\":\"The first homology of a real cubic is generated by lines\",\"authors\":\"S. Finashin, V. Kharlamov\",\"doi\":\"10.1090/conm/772/15485\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We suggest a short proof of O.Benoist and O.Wittenberg theorem (arXiv:1907.10859) which states that for each real non-singular cubic hypersurface $X$ of dimension $\\\\ge 2$ the real lines on $X$ generate the whole group $H_1(X(\\\\Bbb R);\\\\Bbb Z/2)$.\",\"PeriodicalId\":296603,\"journal\":{\"name\":\"Topology, Geometry, and Dynamics\",\"volume\":\"3 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2019-11-16\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"3\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Topology, Geometry, and Dynamics\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1090/conm/772/15485\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Topology, Geometry, and Dynamics","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1090/conm/772/15485","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
The first homology of a real cubic is generated by lines
We suggest a short proof of O.Benoist and O.Wittenberg theorem (arXiv:1907.10859) which states that for each real non-singular cubic hypersurface $X$ of dimension $\ge 2$ the real lines on $X$ generate the whole group $H_1(X(\Bbb R);\Bbb Z/2)$.
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