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arXiv · 2102.08525

A Cayley-Bacharach theorem and plane configurations

Jake Levinson·Brooke Ullery
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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.

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Jake Levinson, Brooke Ullery. 2021-02-17. A Cayley-Bacharach theorem and plane configurations. https://arxiv.org/abs/2102.08525

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