{"title":"有限低阶相交超曲面全纯曲线的缺陷关系","authors":"Nguyen Viet Phuong , Ta Thi Hoai An","doi":"10.1016/j.jmaa.2024.129086","DOIUrl":null,"url":null,"abstract":"<div><div>In this paper, we will give a better upper bound for the defect relation for a class of holomorphic maps, this result is generalized to hypersurfaces from the hyperplane case in <span><span>[9]</span></span>. More precisely, let <span><math><msub><mrow><mi>D</mi></mrow><mrow><mn>1</mn></mrow></msub><mo>,</mo><msub><mrow><mi>D</mi></mrow><mrow><mn>2</mn></mrow></msub><mo>,</mo><mo>.</mo><mo>.</mo><mo>.</mo><mo>,</mo><msub><mrow><mi>D</mi></mrow><mrow><mi>q</mi></mrow></msub></math></span> be hypersurfaces in general position, and let <span><math><mi>f</mi><mo>:</mo><mi>C</mi><mo>→</mo><msup><mrow><mi>P</mi></mrow><mrow><mi>n</mi></mrow></msup><mo>(</mo><mi>C</mi><mo>)</mo></math></span> be holomorphic map of lower order <em>μ</em>, such that <span><math><mi>f</mi><mo>(</mo><mi>C</mi><mo>)</mo><mo>⊄</mo><msub><mrow><mi>D</mi></mrow><mrow><mi>i</mi></mrow></msub></math></span> for all <span><math><mi>i</mi><mo>=</mo><mn>1</mn><mo>,</mo><mn>2</mn><mo>,</mo><mo>.</mo><mo>.</mo><mo>.</mo><mo>,</mo><mi>q</mi></math></span>. If <span><math><mn>0</mn><mo><</mo><mi>μ</mi><mo>≤</mo><mn>1</mn><mo>/</mo><mn>2</mn></math></span> then<span><span><span><math><munderover><mo>∑</mo><mrow><mi>i</mi><mo>=</mo><mn>1</mn></mrow><mrow><mi>q</mi></mrow></munderover><msub><mrow><mi>δ</mi></mrow><mrow><mi>f</mi></mrow></msub><mo>(</mo><msub><mrow><mi>D</mi></mrow><mrow><mi>i</mi></mrow></msub><mo>)</mo><mo>≤</mo><mi>n</mi><mo>.</mo></math></span></span></span></div></div>","PeriodicalId":50147,"journal":{"name":"Journal of Mathematical Analysis and Applications","volume":"544 2","pages":"Article 129086"},"PeriodicalIF":1.2000,"publicationDate":"2024-11-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Defect relations for holomorphic curves of finite lower order intersecting hypersurfaces\",\"authors\":\"Nguyen Viet Phuong , Ta Thi Hoai An\",\"doi\":\"10.1016/j.jmaa.2024.129086\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><div>In this paper, we will give a better upper bound for the defect relation for a class of holomorphic maps, this result is generalized to hypersurfaces from the hyperplane case in <span><span>[9]</span></span>. More precisely, let <span><math><msub><mrow><mi>D</mi></mrow><mrow><mn>1</mn></mrow></msub><mo>,</mo><msub><mrow><mi>D</mi></mrow><mrow><mn>2</mn></mrow></msub><mo>,</mo><mo>.</mo><mo>.</mo><mo>.</mo><mo>,</mo><msub><mrow><mi>D</mi></mrow><mrow><mi>q</mi></mrow></msub></math></span> be hypersurfaces in general position, and let <span><math><mi>f</mi><mo>:</mo><mi>C</mi><mo>→</mo><msup><mrow><mi>P</mi></mrow><mrow><mi>n</mi></mrow></msup><mo>(</mo><mi>C</mi><mo>)</mo></math></span> be holomorphic map of lower order <em>μ</em>, such that <span><math><mi>f</mi><mo>(</mo><mi>C</mi><mo>)</mo><mo>⊄</mo><msub><mrow><mi>D</mi></mrow><mrow><mi>i</mi></mrow></msub></math></span> for all <span><math><mi>i</mi><mo>=</mo><mn>1</mn><mo>,</mo><mn>2</mn><mo>,</mo><mo>.</mo><mo>.</mo><mo>.</mo><mo>,</mo><mi>q</mi></math></span>. If <span><math><mn>0</mn><mo><</mo><mi>μ</mi><mo>≤</mo><mn>1</mn><mo>/</mo><mn>2</mn></math></span> then<span><span><span><math><munderover><mo>∑</mo><mrow><mi>i</mi><mo>=</mo><mn>1</mn></mrow><mrow><mi>q</mi></mrow></munderover><msub><mrow><mi>δ</mi></mrow><mrow><mi>f</mi></mrow></msub><mo>(</mo><msub><mrow><mi>D</mi></mrow><mrow><mi>i</mi></mrow></msub><mo>)</mo><mo>≤</mo><mi>n</mi><mo>.</mo></math></span></span></span></div></div>\",\"PeriodicalId\":50147,\"journal\":{\"name\":\"Journal of Mathematical Analysis and Applications\",\"volume\":\"544 2\",\"pages\":\"Article 129086\"},\"PeriodicalIF\":1.2000,\"publicationDate\":\"2024-11-26\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Journal of Mathematical Analysis and Applications\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://www.sciencedirect.com/science/article/pii/S0022247X24010084\",\"RegionNum\":3,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q1\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Mathematical Analysis and Applications","FirstCategoryId":"100","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0022247X24010084","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS","Score":null,"Total":0}
Defect relations for holomorphic curves of finite lower order intersecting hypersurfaces
In this paper, we will give a better upper bound for the defect relation for a class of holomorphic maps, this result is generalized to hypersurfaces from the hyperplane case in [9]. More precisely, let be hypersurfaces in general position, and let be holomorphic map of lower order μ, such that for all . If then
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