Generalized moment maps, reduction and complex quotients
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866918121039724544 |
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| author | Hu, Yi Wang, Xiangsheng |
| author_facet | Hu, Yi Wang, Xiangsheng |
| contents | In this note, we introduce the concept of momentumly closed forms. A nondegenerate momentumly closed two-form defines a moment map that generalizes the classical notion associated with symplectic forms. We then develop an extended theory of moment maps within this broader framework. More specifically, we establish the convexity property of the generalized moment map, construct the corresponding reduction space, and analyze the Kirwan-Ness stratification. Additionally, we prove a variant of the Darboux-Weinstein theorem for momentumly closed two-forms. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2508_07168 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Generalized moment maps, reduction and complex quotients Hu, Yi Wang, Xiangsheng Differential Geometry Algebraic Geometry Symplectic Geometry 53D20, 14L24 In this note, we introduce the concept of momentumly closed forms. A nondegenerate momentumly closed two-form defines a moment map that generalizes the classical notion associated with symplectic forms. We then develop an extended theory of moment maps within this broader framework. More specifically, we establish the convexity property of the generalized moment map, construct the corresponding reduction space, and analyze the Kirwan-Ness stratification. Additionally, we prove a variant of the Darboux-Weinstein theorem for momentumly closed two-forms. |
| title | Generalized moment maps, reduction and complex quotients |
| topic | Differential Geometry Algebraic Geometry Symplectic Geometry 53D20, 14L24 |
| url | https://arxiv.org/abs/2508.07168 |