Cayley cones ruled by 2-planes: desingularization and implications of the twistor fibration
| dc.creator | Fox, Daniel | |
| dc.date | 2007-09-19 | |
| dc.date | 2008-10-16 | |
| dc.date.accessioned | 2026-07-07T10:10:07Z | |
| dc.date.available | 2026-07-07T10:10:07Z | |
| dc.description | Cayley cones in the octonions $\mathbb{O}$ that are ruled by oriented 2-planes are equivalent to pseudoholomorphic curves in the Grassmannian of oriented 2-planes G(2,8). The well known twistor fibration $G(2,8) -> S^6$ is used to prove the existence of immersed higher-genus pseudoholomorphic curves in $\gro$. Equivalently, this produces Cayley cones whose links are $S^1$-bundles over genus-$g$ Riemann surfaces. When the degree of an immersed pseudoholomorphic curve is large enough, the corresponding 2-ruled Cayley cone is the asymptotic cone of a non-conical 2-ruled Cayley 4-fold. | |
| dc.description | 31 Pages; typos corrected, including Equation 13 and Lemma 6.1; revised exposition; references added | |
| dc.identifier | https://arxiv.org/abs/0709.3115 | |
| dc.identifier | http://arxiv.org/abs/0709.3115 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/171522 | |
| dc.subject | Differential Geometry | |
| dc.subject | 53C38 | |
| dc.title | Cayley cones ruled by 2-planes: desingularization and implications of the twistor fibration | |
| dc.type | text |