Counting projections of rational curves
Algebraic Geometry
2022-05-24 v2
Abstract
Given two general rational curves of the same degree in two projective spaces, one can ask whether there exists a third rational curve of the same degree that projects to both of them. We show that, under suitable assumptions on the degree of the curves and the dimensions of the two given ambient projective spaces, the number of curves and projections fulfilling the requirements is finite. Using standard techniques in intersection theory and the Bott residue formula, we compute this number.
Keywords
Cite
@article{arxiv.1707.05264,
title = {Counting projections of rational curves},
author = {Matteo Gallet and Josef Schicho},
journal= {arXiv preprint arXiv:1707.05264},
year = {2022}
}
Comments
27 pages. This is the accepted version of the manuscript; the published version is available at https://link.springer.com/article/10.1007/s11856-020-2071-3