Hyperkaehler structures on total spaces of holomorphic cotangent bundles
| dc.creator | Kaledin, D. | |
| dc.date | 1997-10-23 | |
| dc.date.accessioned | 2026-07-07T01:51:13Z | |
| dc.date.available | 2026-07-07T01:51:13Z | |
| dc.description | Let $M$ be a Kaehler manifold, and consider the total space $T^*M$ of the cotangent bundle to $M$. We show that in the formal neighborhood of the zero section $M \subset T^*M$ the space $T^*M$ admits a canonical hyperkaehler structure, compatible with the complex and holomorphic symplectic structures on $T^*M$. The associated hyperkaehler metric $h$ coincides with the given Kaehler metric on the zero section $M \subset T^*M$. Moreover, $h$ is invariant under the canonical circle action on $T^*M$ by dilatations along the fibers of $T^*M$ over $M$. We show that a hyperkaehler structure with these properties is unique. When the Kaehler metric on $M$ is real-analytic, we show that this formal hyperkaehler structure can be extended to an open neighborhood of the zero section. We also prove a hyperkaehler analog of the Darboux-Weinstein Theorem. To prove these results, we use the machinery of $R$-Hodge structures, following Deligne and Simpson. | |
| dc.description | 100 pages, LaTeX2e | |
| dc.identifier | https://arxiv.org/abs/alg-geom/9710026 | |
| dc.identifier | http://arxiv.org/abs/alg-geom/9710026 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/242 | |
| dc.subject | Algebraic Geometry | |
| dc.title | Hyperkaehler structures on total spaces of holomorphic cotangent bundles | |
| dc.type | text |