# Twistor lines on algebraic surfaces

created by altavilla on 09 Mar 2018
modified on 11 Mar 2019

[BibTeX]

in press

Inserted: 9 mar 2018
Last Updated: 11 mar 2019

Journal: Annals of Global Analysis and Geometry
Year: 2018
Doi: https://doi.org/10.1007/s10455-018-9640-2

ArXiv: 1802.06697v2 PDF
We give quantitative and qualitative results on the family of surfaces in $\mathbb{CP}^3$ containing finitely many twistor lines. We start by analyzing the ideal sheaf of a finite set of disjoint lines E. We prove that its general element is a smooth surface containing E and no other line. Afterward we prove that twistor lines are Zariski dense in the Grassmannian $Gr(2, 4)$. Then, for any degree $d\geq 4$ , we give lower bounds on the maximum number of twistor lines contained in a degree d surface. The smooth and singular cases are studied as well as the $j$-invariant one.