{"title":"紧K\\ ahler流形上幂偶群的哈密顿作用","authors":"D. Greb, C. Miebach","doi":"10.46298/epiga.2018.volume2.4486","DOIUrl":null,"url":null,"abstract":"We study meromorphic actions of unipotent complex Lie groups on compact\nK\\\"ahler manifolds using moment map techniques. We introduce natural stability\nconditions and show that sets of semistable points are Zariski-open and admit\ngeometric quotients that carry compactifiable K\\\"ahler structures obtained by\nsymplectic reduction. The relation of our complex-analytic theory to the work\nof Doran--Kirwan regarding the Geometric Invariant Theory of unipotent group\nactions on projective varieties is discussed in detail.\n\n Comment: v2: 30 pages, final version as accepted by EPIGA","PeriodicalId":41470,"journal":{"name":"Epijournal de Geometrie Algebrique","volume":"1 1","pages":""},"PeriodicalIF":0.9000,"publicationDate":"2018-05-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"2","resultStr":"{\"title\":\"Hamiltonian actions of unipotent groups on compact K\\\\\\\"ahler manifolds\",\"authors\":\"D. Greb, C. Miebach\",\"doi\":\"10.46298/epiga.2018.volume2.4486\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We study meromorphic actions of unipotent complex Lie groups on compact\\nK\\\\\\\"ahler manifolds using moment map techniques. We introduce natural stability\\nconditions and show that sets of semistable points are Zariski-open and admit\\ngeometric quotients that carry compactifiable K\\\\\\\"ahler structures obtained by\\nsymplectic reduction. The relation of our complex-analytic theory to the work\\nof Doran--Kirwan regarding the Geometric Invariant Theory of unipotent group\\nactions on projective varieties is discussed in detail.\\n\\n Comment: v2: 30 pages, final version as accepted by EPIGA\",\"PeriodicalId\":41470,\"journal\":{\"name\":\"Epijournal de Geometrie Algebrique\",\"volume\":\"1 1\",\"pages\":\"\"},\"PeriodicalIF\":0.9000,\"publicationDate\":\"2018-05-07\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"2\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Epijournal de Geometrie Algebrique\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.46298/epiga.2018.volume2.4486\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q2\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Epijournal de Geometrie Algebrique","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.46298/epiga.2018.volume2.4486","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS","Score":null,"Total":0}
Hamiltonian actions of unipotent groups on compact K\"ahler manifolds
We study meromorphic actions of unipotent complex Lie groups on compact
K\"ahler manifolds using moment map techniques. We introduce natural stability
conditions and show that sets of semistable points are Zariski-open and admit
geometric quotients that carry compactifiable K\"ahler structures obtained by
symplectic reduction. The relation of our complex-analytic theory to the work
of Doran--Kirwan regarding the Geometric Invariant Theory of unipotent group
actions on projective varieties is discussed in detail.
Comment: v2: 30 pages, final version as accepted by EPIGA
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