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arXiv · 2305.15651

Kirwan surjectivity and Lefschetz-Sommese theorems for a generalized hyperk\"ahler reduction

Jonathan Fisher·Lisa Jeffrey·Alessandro Malusà·Steven Rayan
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Abstract

Let $G$ be a compact Lie group. We study a class of Hamiltonian $(G \times S^{1})$-manifolds decorated with a function $s$ with certain equivariance properties, under conditions on the $G$-action which we call of (semi-)linear type. In this context, a close analogue of hyperk\"ahler reduction is defined, and our main result establishes surjectivity of an appropriate analogue of Kirwan's map. As a particular case, our setting includes a class of hyperk\"ahler manifolds with trihamiltonian torus actions, to which our surjectivity result applies.

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Jonathan Fisher, Lisa Jeffrey, Alessandro Malusà, Steven Rayan. 2023-05-25. Kirwan surjectivity and Lefschetz-Sommese theorems for a generalized hyperk\"ahler reduction. https://doi.org/10.1007/s10711-023-00831-w

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