{"title":"平面分支的二临界叶形和半根","authors":"","doi":"10.1016/j.exmath.2024.125591","DOIUrl":null,"url":null,"abstract":"<div><p>In this work we describe dicritical foliations in <span><math><mrow><mo>(</mo><msup><mrow><mi>ℂ</mi></mrow><mrow><mn>2</mn></mrow></msup><mo>,</mo><mn>0</mn><mo>)</mo></mrow></math></span> at a triple point of the resolution dual graph of an analytic plane branch <span><math><mi>C</mi></math></span> using its semiroots. In particular, we obtain a constructive method to present a one-parameter family <span><math><msub><mrow><mi>C</mi></mrow><mrow><mi>u</mi></mrow></msub></math></span> of separatrices for such foliations. As a by-product we relate the contact order between a special member of <span><math><msub><mrow><mi>C</mi></mrow><mrow><mi>u</mi></mrow></msub></math></span> and <span><math><mi>C</mi></math></span> with analytic discrete invariants of plane branches.</p></div>","PeriodicalId":50458,"journal":{"name":"Expositiones Mathematicae","volume":null,"pages":null},"PeriodicalIF":0.8000,"publicationDate":"2024-07-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S0723086924000586/pdfft?md5=3299d7524f5c5d739013dc887d4e9582&pid=1-s2.0-S0723086924000586-main.pdf","citationCount":"0","resultStr":"{\"title\":\"Dicritical foliations and semiroots of plane branches\",\"authors\":\"\",\"doi\":\"10.1016/j.exmath.2024.125591\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><p>In this work we describe dicritical foliations in <span><math><mrow><mo>(</mo><msup><mrow><mi>ℂ</mi></mrow><mrow><mn>2</mn></mrow></msup><mo>,</mo><mn>0</mn><mo>)</mo></mrow></math></span> at a triple point of the resolution dual graph of an analytic plane branch <span><math><mi>C</mi></math></span> using its semiroots. In particular, we obtain a constructive method to present a one-parameter family <span><math><msub><mrow><mi>C</mi></mrow><mrow><mi>u</mi></mrow></msub></math></span> of separatrices for such foliations. As a by-product we relate the contact order between a special member of <span><math><msub><mrow><mi>C</mi></mrow><mrow><mi>u</mi></mrow></msub></math></span> and <span><math><mi>C</mi></math></span> with analytic discrete invariants of plane branches.</p></div>\",\"PeriodicalId\":50458,\"journal\":{\"name\":\"Expositiones Mathematicae\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.8000,\"publicationDate\":\"2024-07-18\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"https://www.sciencedirect.com/science/article/pii/S0723086924000586/pdfft?md5=3299d7524f5c5d739013dc887d4e9582&pid=1-s2.0-S0723086924000586-main.pdf\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Expositiones Mathematicae\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://www.sciencedirect.com/science/article/pii/S0723086924000586\",\"RegionNum\":4,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q2\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Expositiones Mathematicae","FirstCategoryId":"100","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0723086924000586","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS","Score":null,"Total":0}
Dicritical foliations and semiroots of plane branches
In this work we describe dicritical foliations in at a triple point of the resolution dual graph of an analytic plane branch using its semiroots. In particular, we obtain a constructive method to present a one-parameter family of separatrices for such foliations. As a by-product we relate the contact order between a special member of and with analytic discrete invariants of plane branches.
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