2-平面控制的Cayley锥：扭量纤维化的去奇异化和意义
Cayley cones ruled by 2-planes: desingularization and implications of the twistor fibration
摘要：
八元数$\mathbb{O}$中由定向2-平面刻划的凯莱锥等价于定向2-平面G（2，8）中的格拉斯曼曲线。利用著名的扭量纤维化$G(2,8) -> S^6$证明了$\gro$中浸入的高亏格拟全纯曲线的存在性.等价地，这产生Cayley锥，其连接是亏格- $g$黎曼曲面上的$S^1$ -丛。当浸入伪全纯曲线的次数足够大时，对应的2-直纹Cayley锥是非锥2-直纹Cayley 4-重的渐近锥面.
英文摘要：
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.
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