{"title":"表面","authors":"Thibaut Fourcade","doi":"10.51257/a-v2-tba115","DOIUrl":null,"url":null,"abstract":". Let Cox( S r ) be the homogeneous coordinate ring of the blow-up S r of P 2 in r general points, i.e., a smooth Del Pezzo surface of degree 9 − r . We prove that for r ∈ { 6 , 7 } , Proj(Cox( S r )) can be embedded into G r /P r , where G r is an algebraic group with root system given by the primitive Picard lattice of S r and P r ⊂ G r is a certain maximal parabolic subgroup.","PeriodicalId":344219,"journal":{"name":"Techniques du bâtiment : Unités conventionnelles et formules","volume":"195 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2022-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Surfaces\",\"authors\":\"Thibaut Fourcade\",\"doi\":\"10.51257/a-v2-tba115\",\"DOIUrl\":null,\"url\":null,\"abstract\":\". Let Cox( S r ) be the homogeneous coordinate ring of the blow-up S r of P 2 in r general points, i.e., a smooth Del Pezzo surface of degree 9 − r . We prove that for r ∈ { 6 , 7 } , Proj(Cox( S r )) can be embedded into G r /P r , where G r is an algebraic group with root system given by the primitive Picard lattice of S r and P r ⊂ G r is a certain maximal parabolic subgroup.\",\"PeriodicalId\":344219,\"journal\":{\"name\":\"Techniques du bâtiment : Unités conventionnelles et formules\",\"volume\":\"195 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2022-05-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Techniques du bâtiment : Unités conventionnelles et formules\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.51257/a-v2-tba115\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Techniques du bâtiment : Unités conventionnelles et formules","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.51257/a-v2-tba115","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
. Let Cox( S r ) be the homogeneous coordinate ring of the blow-up S r of P 2 in r general points, i.e., a smooth Del Pezzo surface of degree 9 − r . We prove that for r ∈ { 6 , 7 } , Proj(Cox( S r )) can be embedded into G r /P r , where G r is an algebraic group with root system given by the primitive Picard lattice of S r and P r ⊂ G r is a certain maximal parabolic subgroup.
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