Simone Marchesi, Alex Massarenti, Saeed Tafazolian
{"title":"COVERED BY LINES AND CONIC CONNECTED VARIETIES","authors":"Simone Marchesi, Alex Massarenti, Saeed Tafazolian","doi":"10.4418/2011.66.2.12","DOIUrl":null,"url":null,"abstract":"We study some properties of an embedded variety covered by lines and give a numerical criterion ensuring the existence of a singular conic through two of its general points. We show that our criterion is sharp. Conic-connected, covered by lines, QEL, LQEL, prime Fano, defective, and dual defective varieties are closely related. We study some relations between the above mentioned classes of objects using basic results by Ein and Zak.","PeriodicalId":107618,"journal":{"name":"Le Matematiche","volume":"3 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2011-05-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"3","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Le Matematiche","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.4418/2011.66.2.12","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 3
Abstract
We study some properties of an embedded variety covered by lines and give a numerical criterion ensuring the existence of a singular conic through two of its general points. We show that our criterion is sharp. Conic-connected, covered by lines, QEL, LQEL, prime Fano, defective, and dual defective varieties are closely related. We study some relations between the above mentioned classes of objects using basic results by Ein and Zak.
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