{"title":"多项式应用的拓扑不变量","authors":"Enrique Artal Bartolo , Pierrette Cassou-Noguès , Hélène Maugendre","doi":"10.1016/S0764-4442(01)02093-6","DOIUrl":null,"url":null,"abstract":"<div><p>Let <span><math><mtext>φ:=(f,g):</mtext><mtext>C</mtext><msup><mi></mi><mn>2</mn></msup><mtext>→</mtext><mtext>C</mtext><msup><mi></mi><mn>2</mn></msup></math></span> with <em>f</em> and <em>g</em> polynomial mappings. We establish the connection that exists between the Newton polygon of the curve which is the union of the discriminant and of the non-proper locus of <em>φ</em> and the topology of the links at infinity of the curves <em>f</em><sup>−1</sup>(0) and <em>g</em><sup>−1</sup>(0).</p></div>","PeriodicalId":100300,"journal":{"name":"Comptes Rendus de l'Académie des Sciences - Series I - Mathematics","volume":"333 8","pages":"Pages 751-754"},"PeriodicalIF":0.0000,"publicationDate":"2001-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1016/S0764-4442(01)02093-6","citationCount":"0","resultStr":"{\"title\":\"Invariants topologiques d'applications polynomiales\",\"authors\":\"Enrique Artal Bartolo , Pierrette Cassou-Noguès , Hélène Maugendre\",\"doi\":\"10.1016/S0764-4442(01)02093-6\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><p>Let <span><math><mtext>φ:=(f,g):</mtext><mtext>C</mtext><msup><mi></mi><mn>2</mn></msup><mtext>→</mtext><mtext>C</mtext><msup><mi></mi><mn>2</mn></msup></math></span> with <em>f</em> and <em>g</em> polynomial mappings. We establish the connection that exists between the Newton polygon of the curve which is the union of the discriminant and of the non-proper locus of <em>φ</em> and the topology of the links at infinity of the curves <em>f</em><sup>−1</sup>(0) and <em>g</em><sup>−1</sup>(0).</p></div>\",\"PeriodicalId\":100300,\"journal\":{\"name\":\"Comptes Rendus de l'Académie des Sciences - Series I - Mathematics\",\"volume\":\"333 8\",\"pages\":\"Pages 751-754\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2001-10-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"https://sci-hub-pdf.com/10.1016/S0764-4442(01)02093-6\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Comptes Rendus de l'Académie des Sciences - Series I - Mathematics\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://www.sciencedirect.com/science/article/pii/S0764444201020936\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Comptes Rendus de l'Académie des Sciences - Series I - Mathematics","FirstCategoryId":"1085","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0764444201020936","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Let with f and g polynomial mappings. We establish the connection that exists between the Newton polygon of the curve which is the union of the discriminant and of the non-proper locus of φ and the topology of the links at infinity of the curves f−1(0) and g−1(0).
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