Cayley cones ruled by 2-planes: desingularization and implications of the twistor fibration

dc.creatorFox, Daniel
dc.date2007-09-19
dc.date2008-10-16
dc.date.accessioned2026-07-07T10:10:07Z
dc.date.available2026-07-07T10:10:07Z
dc.descriptionCayley 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.description31 Pages; typos corrected, including Equation 13 and Lemma 6.1; revised exposition; references added
dc.identifierhttps://arxiv.org/abs/0709.3115
dc.identifierhttp://arxiv.org/abs/0709.3115
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/171522
dc.subjectDifferential Geometry
dc.subject53C38
dc.titleCayley cones ruled by 2-planes: desingularization and implications of the twistor fibration
dc.typetext

Files

Collections