. 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.
{"title":"Surfaces","authors":"Thibaut Fourcade","doi":"10.51257/a-v2-tba115","DOIUrl":"https://doi.org/10.51257/a-v2-tba115","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":0.0,"publicationDate":"2022-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"121740623","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}
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