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.

7 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