A Cayley-Bacharach theorem and plane configurations
Algebraic Geometry
2022-01-07 v2
Abstract
In this paper, we examine linear conditions on finite sets of points in projective space implied by the Cayley-Bacharach condition. In particular, by bounding the number of points satisfying the Cayley-Bacharach condition, we force them to lie on unions of low-dimensional linear spaces. These results are motivated by investigations into degrees of irrationality of complete intersections, which are controlled by minimum-degree rational maps to projective space. As an application of our main theorem, we describe the fibers of such maps for certain complete intersections of codimension two.
Cite
@article{arxiv.2102.08525,
title = {A Cayley-Bacharach theorem and plane configurations},
author = {Jake Levinson and Brooke Ullery},
journal= {arXiv preprint arXiv:2102.08525},
year = {2022}
}
Comments
Final version to appear in Proc. AMS. We also corrected and improved Theorem 1.4 and Proposition 1.6