Generalized moment maps, reduction and complex quotients

Yi Hu; Xiangsheng Wang

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arXiv · 2508.07168

Generalized moment maps, reduction and complex quotients

Yi Hu·Xiangsheng Wang

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Abstract

In this note, we introduce the concept of momentumly closed forms. A non-degenerate momentumly closed two-form and its generalized moment map are the generalization of two well-known notions, symplectic forms and moment maps, in the almost Hermitian setting. We then generalize the classical theory of moment maps to this broader framework. As a first step, we prove a variant of the Darboux-Weinstein theorem for non-degenerate momentumly closed two-forms. Based on this, we further establish the convexity property of the generalized moment map, construct the corresponding reduction space and investigate the properties of the Kirwan-Ness stratification.

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Yi Hu, Xiangsheng Wang. 2025-08-10. Generalized moment maps, reduction and complex quotients. https://arxiv.org/abs/2508.07168

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