{"title":"可积系统和特殊Kähler度量","authors":"N. Hitchin","doi":"10.4171/emss/46","DOIUrl":null,"url":null,"abstract":"We describe the Special Kahler structure on the base of the so-called Hitchin system in terms of the geometry of the space of spectral curves. It yields a simple formula for the Kahler potential. This extends to the case of a singular spectral curve and we show that this defines the Special Kahler structure on certain natural integrable subsystems. Examples include the extreme case where the metric is flat.","PeriodicalId":43833,"journal":{"name":"EMS Surveys in Mathematical Sciences","volume":null,"pages":null},"PeriodicalIF":1.3000,"publicationDate":"2019-10-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"1","resultStr":"{\"title\":\"Integrable systems and Special Kähler metrics\",\"authors\":\"N. Hitchin\",\"doi\":\"10.4171/emss/46\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We describe the Special Kahler structure on the base of the so-called Hitchin system in terms of the geometry of the space of spectral curves. It yields a simple formula for the Kahler potential. This extends to the case of a singular spectral curve and we show that this defines the Special Kahler structure on certain natural integrable subsystems. Examples include the extreme case where the metric is flat.\",\"PeriodicalId\":43833,\"journal\":{\"name\":\"EMS Surveys in Mathematical Sciences\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":1.3000,\"publicationDate\":\"2019-10-11\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"1\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"EMS Surveys in Mathematical Sciences\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.4171/emss/46\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q1\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"EMS Surveys in Mathematical Sciences","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.4171/emss/46","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS","Score":null,"Total":0}
We describe the Special Kahler structure on the base of the so-called Hitchin system in terms of the geometry of the space of spectral curves. It yields a simple formula for the Kahler potential. This extends to the case of a singular spectral curve and we show that this defines the Special Kahler structure on certain natural integrable subsystems. Examples include the extreme case where the metric is flat.
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