Kirwan surjectivity and Lefschetz-Sommese theorems for a generalized hyperkähler reduction
Fuente:
arXiv
Saved in:
| Main Authors: | , , , |
|---|---|
| Format: | Preprint |
| Published: |
2023
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866929370383253504 |
|---|---|
| author | Fisher, Jonathan Jeffrey, Lisa Malusà, Alessandro Rayan, Steven |
| author_facet | Fisher, Jonathan Jeffrey, Lisa Malusà, Alessandro Rayan, Steven |
| contents | 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 hyperkähler 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 hyperkähler manifolds with trihamiltonian torus actions, to which our surjectivity result applies. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2305_15651 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Kirwan surjectivity and Lefschetz-Sommese theorems for a generalized hyperkähler reduction Fisher, Jonathan Jeffrey, Lisa Malusà, Alessandro Rayan, Steven Symplectic Geometry Algebraic Geometry Algebraic Topology Differential Geometry 53D20, 53C26, 57R91 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 hyperkähler 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 hyperkähler manifolds with trihamiltonian torus actions, to which our surjectivity result applies. |
| title | Kirwan surjectivity and Lefschetz-Sommese theorems for a generalized hyperkähler reduction |
| topic | Symplectic Geometry Algebraic Geometry Algebraic Topology Differential Geometry 53D20, 53C26, 57R91 |
| url | https://arxiv.org/abs/2305.15651 |