Hyperkahler analogues of Kahler quotients
| dc.creator | Proudfoot, Nicholas J. | |
| dc.date | 2004-05-12 | |
| dc.date.accessioned | 2026-07-07T05:08:11Z | |
| dc.date.available | 2026-07-07T05:08:11Z | |
| dc.description | Let X be a Kahler manifold that is presented as a Kahler quotient of C^n by the linear action of a compact group G. We define the hyperkahler analogue M of X as a hyperkahler quotient of the cotangent bundle T^*C^n by the induced G-action. Special instances of this construction include hypertoric varieties and quiver varieties. Our aim is to provide a unified treatment of these two previously studied examples, with specific attention to the geometry and topology of the circle action on M that descends from the scalar action on the fibers of the cotangent bundle. We provide a detailed study of this action in the cases where M is a hypertoric variety or a hyperpolygon space. Most of this document consists of material from the papers math.DG/0207012, math.AG/0308218, and math.SG/0310141. Sections 2.2 and 3.5 contain previously unannounced results. | |
| dc.description | 86 pages, 10 figures | |
| dc.identifier | https://arxiv.org/abs/math/0405233 | |
| dc.identifier | http://arxiv.org/abs/math/0405233 | |
| dc.identifier | Ph. D. thesis, U.C. Berkeley, Spring 2004 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/71165 | |
| dc.subject | Algebraic Geometry | |
| dc.subject | Differential Geometry | |
| dc.subject | Symplectic Geometry | |
| dc.subject | 53C26; 53D20; 14D20; 52C35 | |
| dc.title | Hyperkahler analogues of Kahler quotients | |
| dc.type | text |