Algebraic surfaces with infinitely many twistor lines
Differential Geometry
2021-12-22 v2 Algebraic Geometry
Complex Variables
Abstract
We prove that a reduced and irreducible algebraic surface in 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.
Cite
@article{arxiv.1902.00010,
title = {Algebraic surfaces with infinitely many twistor lines},
author = {Amedeo Altavilla and Edoardo Ballico},
journal= {arXiv preprint arXiv:1902.00010},
year = {2021}
}
Comments
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