Twistor fibers in hypersurfaces of the flag threefold
Algebraic Geometry
2023-10-31 v2 Complex Variables
Differential Geometry
Abstract
We study surfaces of bidegree (1,d) contained in the flag threefold in relation to the twistor projection. In particular, we focus on the number and the arrangement of twistor fibers contained in such surfaces. First, we prove that there is no irreducible surface of bidegree (1,d) containing d+2 twistor fibers in general position. On the other hand, given any collection of (d+1) twistor fibers satisfying a mild natural constraint, we prove the existence of a surface of bidegree (1,d) that contains them. We improve our results for d=2 or d=3, by removing all the generality hypotheses.
Cite
@article{arxiv.2301.04874,
title = {Twistor fibers in hypersurfaces of the flag threefold},
author = {Amedeo Altavilla and Edoardo Ballico and Maria Chiara Brambilla},
journal= {arXiv preprint arXiv:2301.04874},
year = {2023}
}
Comments
1 figure. Title, abstract and introduction updated. Published on New York Journal of Mathematics: https://nyjm.albany.edu/j/2023/29-45.html