{"title":"低阶超曲面的复曲面退化","authors":"N. Ilten, Oscar Lautsch","doi":"10.4153/s0008439523000309","DOIUrl":null,"url":null,"abstract":"Abstract We show that a sufficiently general hypersurface of degree d in \n$\\mathbb {P}^n$\n admits a toric Gröbner degeneration after linear change of coordinates if and only if \n$d\\leq 2n-1$\n .","PeriodicalId":0,"journal":{"name":"","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2022-08-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"TORIC DEGENERATIONS OF LOW DEGREE HYPERSURFACES\",\"authors\":\"N. Ilten, Oscar Lautsch\",\"doi\":\"10.4153/s0008439523000309\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Abstract We show that a sufficiently general hypersurface of degree d in \\n$\\\\mathbb {P}^n$\\n admits a toric Gröbner degeneration after linear change of coordinates if and only if \\n$d\\\\leq 2n-1$\\n .\",\"PeriodicalId\":0,\"journal\":{\"name\":\"\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.0,\"publicationDate\":\"2022-08-24\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.4153/s0008439523000309\",\"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/10.4153/s0008439523000309","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Abstract We show that a sufficiently general hypersurface of degree d in
$\mathbb {P}^n$
admits a toric Gröbner degeneration after linear change of coordinates if and only if
$d\leq 2n-1$
.
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