{"title":"是什么使复合体成为虚拟分辨率?","authors":"Michael C. Loper","doi":"10.1090/btran/91","DOIUrl":null,"url":null,"abstract":"Virtual resolutions are homological representations of finitely generated \n\n \n \n Pic\n (\n X\n )\n \n \\text {Pic}(X)\n \n\n-graded modules over the Cox ring of a smooth projective toric variety. In this paper, we identify two algebraic conditions that characterize when a chain complex of graded free modules over the Cox ring is a virtual resolution. We then turn our attention to the saturation of Fitting ideals by the irrelevant ideal of the Cox ring and prove some results that mirror the classical theory of Fitting ideals for Noetherian rings.","PeriodicalId":377306,"journal":{"name":"Transactions of the American Mathematical Society, Series B","volume":"63 2 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2019-04-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"11","resultStr":"{\"title\":\"What makes a complex a virtual resolution?\",\"authors\":\"Michael C. Loper\",\"doi\":\"10.1090/btran/91\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Virtual resolutions are homological representations of finitely generated \\n\\n \\n \\n Pic\\n (\\n X\\n )\\n \\n \\\\text {Pic}(X)\\n \\n\\n-graded modules over the Cox ring of a smooth projective toric variety. In this paper, we identify two algebraic conditions that characterize when a chain complex of graded free modules over the Cox ring is a virtual resolution. We then turn our attention to the saturation of Fitting ideals by the irrelevant ideal of the Cox ring and prove some results that mirror the classical theory of Fitting ideals for Noetherian rings.\",\"PeriodicalId\":377306,\"journal\":{\"name\":\"Transactions of the American Mathematical Society, Series B\",\"volume\":\"63 2 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2019-04-12\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"11\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Transactions of the American Mathematical Society, Series B\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1090/btran/91\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Transactions of the American Mathematical Society, Series B","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1090/btran/91","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Virtual resolutions are homological representations of finitely generated
Pic
(
X
)
\text {Pic}(X)
-graded modules over the Cox ring of a smooth projective toric variety. In this paper, we identify two algebraic conditions that characterize when a chain complex of graded free modules over the Cox ring is a virtual resolution. We then turn our attention to the saturation of Fitting ideals by the irrelevant ideal of the Cox ring and prove some results that mirror the classical theory of Fitting ideals for Noetherian rings.
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