{"title":"开阔曲线上局部系统的孪生空间","authors":"Carlos T. Simpson","doi":"10.1142/s0129167x24410131","DOIUrl":null,"url":null,"abstract":"<p>Let <span><math altimg=\"eq-00001.gif\" display=\"inline\" overflow=\"scroll\"><mi>X</mi><mo>=</mo><mover accent=\"false\"><mrow><mi>X</mi></mrow><mo accent=\"true\">¯</mo></mover><mo stretchy=\"false\">−</mo><mi>D</mi></math></span><span></span> be a smooth quasi-projective curve. We previously constructed a Deligne–Hitchin moduli space with Hecke gauge groupoid for connections of rank <span><math altimg=\"eq-00002.gif\" display=\"inline\" overflow=\"scroll\"><mn>2</mn></math></span><span></span>. We extend this construction to the case of any rank <span><math altimg=\"eq-00003.gif\" display=\"inline\" overflow=\"scroll\"><mi>r</mi></math></span><span></span>, although still keeping a genericity hypothesis. The formal neighborhood of a preferred section corresponding to a tame harmonic bundle is governed by a mixed twistor structure.</p>","PeriodicalId":54951,"journal":{"name":"International Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":0.6000,"publicationDate":"2024-03-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Twistor space for local systems on an open curve\",\"authors\":\"Carlos T. Simpson\",\"doi\":\"10.1142/s0129167x24410131\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<p>Let <span><math altimg=\\\"eq-00001.gif\\\" display=\\\"inline\\\" overflow=\\\"scroll\\\"><mi>X</mi><mo>=</mo><mover accent=\\\"false\\\"><mrow><mi>X</mi></mrow><mo accent=\\\"true\\\">¯</mo></mover><mo stretchy=\\\"false\\\">−</mo><mi>D</mi></math></span><span></span> be a smooth quasi-projective curve. We previously constructed a Deligne–Hitchin moduli space with Hecke gauge groupoid for connections of rank <span><math altimg=\\\"eq-00002.gif\\\" display=\\\"inline\\\" overflow=\\\"scroll\\\"><mn>2</mn></math></span><span></span>. We extend this construction to the case of any rank <span><math altimg=\\\"eq-00003.gif\\\" display=\\\"inline\\\" overflow=\\\"scroll\\\"><mi>r</mi></math></span><span></span>, although still keeping a genericity hypothesis. The formal neighborhood of a preferred section corresponding to a tame harmonic bundle is governed by a mixed twistor structure.</p>\",\"PeriodicalId\":54951,\"journal\":{\"name\":\"International Journal of Mathematics\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.6000,\"publicationDate\":\"2024-03-27\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"International Journal of Mathematics\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.1142/s0129167x24410131\",\"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":"International Journal of Mathematics","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1142/s0129167x24410131","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"MATHEMATICS","Score":null,"Total":0}
Let be a smooth quasi-projective curve. We previously constructed a Deligne–Hitchin moduli space with Hecke gauge groupoid for connections of rank . We extend this construction to the case of any rank , although still keeping a genericity hypothesis. The formal neighborhood of a preferred section corresponding to a tame harmonic bundle is governed by a mixed twistor structure.
期刊介绍：
The International Journal of Mathematics publishes original papers in mathematics in general, but giving a preference to those in the areas of mathematics represented by the editorial board. The journal has been published monthly except in June and December to bring out new results without delay. Occasionally, expository papers of exceptional value may also be published. The first issue appeared in March 1990.
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