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arXiv · 1710.00407

Fibers of rational maps and Jacobian matrices

Marc Chardin·Steven Dale Cutkosky·Quang Hoa Tran
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Abstract

A rational map $\phi: \mathbb{P}_k^m \dashrightarrow \mathbb{P}_k^n$ is defined by homogeneous polynomials of a common degree $d$. We establish a linear bound in terms of $d$ for the number of $(m-1)$-dimensional fibers of $\phi$, by using ideals of minors of the Jacobian matrix. In particular, we answer affirmatively Question~11 in arXiv:1511.02933v2.

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Marc Chardin, Steven Dale Cutkosky, Quang Hoa Tran. 2017-10-01. Fibers of rational maps and Jacobian matrices. https://doi.org/10.1016/j.jalgebra.2019.01.035

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