{"title":"$$\\textrm{SL}_2(\\mathbb {C})$$自由群字符变化的Fano紧化","authors":"Joseph Cummings, Christopher Manon","doi":"10.1007/s10711-023-00867-y","DOIUrl":null,"url":null,"abstract":"<p>We show that a certain compactification <span>\\(\\mathfrak {X}_g\\)</span> of the <span>\\(\\textrm{SL}_2(\\mathbb {C})\\)</span> free group character variety <span>\\(\\mathcal {X}(F_g, \\textrm{SL}_2(\\mathbb {C}))\\)</span> is Fano. This compactification has been studied previously by the second author, and separately by Biswas, Lawton, and Ramras. Part of the proof of this result involves the construction of a large family of integral reflexive polytopes.\n</p>","PeriodicalId":0,"journal":{"name":"","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-11-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"A Fano compactification of the $$\\\\textrm{SL}_2(\\\\mathbb {C})$$ free group character variety\",\"authors\":\"Joseph Cummings, Christopher Manon\",\"doi\":\"10.1007/s10711-023-00867-y\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<p>We show that a certain compactification <span>\\\\(\\\\mathfrak {X}_g\\\\)</span> of the <span>\\\\(\\\\textrm{SL}_2(\\\\mathbb {C})\\\\)</span> free group character variety <span>\\\\(\\\\mathcal {X}(F_g, \\\\textrm{SL}_2(\\\\mathbb {C}))\\\\)</span> is Fano. This compactification has been studied previously by the second author, and separately by Biswas, Lawton, and Ramras. Part of the proof of this result involves the construction of a large family of integral reflexive polytopes.\\n</p>\",\"PeriodicalId\":0,\"journal\":{\"name\":\"\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.0,\"publicationDate\":\"2023-11-23\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.1007/s10711-023-00867-y\",\"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/10.1007/s10711-023-00867-y","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
A Fano compactification of the $$\textrm{SL}_2(\mathbb {C})$$ free group character variety
We show that a certain compactification \(\mathfrak {X}_g\) of the \(\textrm{SL}_2(\mathbb {C})\) free group character variety \(\mathcal {X}(F_g, \textrm{SL}_2(\mathbb {C}))\) is Fano. This compactification has been studied previously by the second author, and separately by Biswas, Lawton, and Ramras. Part of the proof of this result involves the construction of a large family of integral reflexive polytopes.
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