Algebraic surfaces with infinitely many twistor lines

Abstract

We prove that a reduced and irreducible algebraic surface in ${\mathbb{CP}}^3$ containing infinitely many twistor lines cannot have odd degree. Then, exploiting the theory of quaternionic slice regularity and the normalization map of a surface, we give constructive existence results for even degrees.

arXiv comment7 pages. arXiv admin note: substantial text overlap with arXiv:1802.06697. This paper was extracted from the last section of arXiv:1802.06697v2, where a question was left open. For this reason most of the material is the same

References in corpus (9)

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• Slice-Polynomial Functions and Twistor Geometry of Ruled Surfaces in ${\mathbb{CP}}^3$
• Twistor lines on cubic surfaces
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Cited by in corpus (3)

• Twistor geometry of the Flag manifold
• Three Topological Results on the Twistor Discriminant Locus in the 4-Sphere
• Surfaces in the flag threefold containing smooth conics and twistor fibers