{"title":"二元和三元形式的联合微分不变量","authors":"G. Polat, P. Olver","doi":"10.4171/pm/2032","DOIUrl":null,"url":null,"abstract":"We use moving frames to construct and classify the joint invariants and joint differential invariants of binary and ternary forms. In particular, we prove that the differential invariant algebra of ternary forms is generated by a single third order differential invariant. To connect our results with earlier analysis of Kogan, we develop a general method for relating differential invariants associated with different choices of cross-section.","PeriodicalId":51269,"journal":{"name":"Portugaliae Mathematica","volume":"76 1","pages":"169-204"},"PeriodicalIF":0.5000,"publicationDate":"2020-02-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.4171/pm/2032","citationCount":"4","resultStr":"{\"title\":\"Joint differential invariants of binary and ternary forms\",\"authors\":\"G. Polat, P. Olver\",\"doi\":\"10.4171/pm/2032\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We use moving frames to construct and classify the joint invariants and joint differential invariants of binary and ternary forms. In particular, we prove that the differential invariant algebra of ternary forms is generated by a single third order differential invariant. To connect our results with earlier analysis of Kogan, we develop a general method for relating differential invariants associated with different choices of cross-section.\",\"PeriodicalId\":51269,\"journal\":{\"name\":\"Portugaliae Mathematica\",\"volume\":\"76 1\",\"pages\":\"169-204\"},\"PeriodicalIF\":0.5000,\"publicationDate\":\"2020-02-13\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"https://sci-hub-pdf.com/10.4171/pm/2032\",\"citationCount\":\"4\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Portugaliae Mathematica\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.4171/pm/2032\",\"RegionNum\":4,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q3\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Portugaliae Mathematica","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.4171/pm/2032","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"MATHEMATICS","Score":null,"Total":0}
Joint differential invariants of binary and ternary forms
We use moving frames to construct and classify the joint invariants and joint differential invariants of binary and ternary forms. In particular, we prove that the differential invariant algebra of ternary forms is generated by a single third order differential invariant. To connect our results with earlier analysis of Kogan, we develop a general method for relating differential invariants associated with different choices of cross-section.
期刊介绍：
Since its foundation in 1937, Portugaliae Mathematica has aimed at publishing high-level research articles in all branches of mathematics. With great efforts by its founders, the journal was able to publish articles by some of the best mathematicians of the time. In 2001 a New Series of Portugaliae Mathematica was started, reaffirming the purpose of maintaining a high-level research journal in mathematics with a wide range scope.
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