Fibers of rational maps and Jacobian matrices
نویسندگان
چکیده
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 linear bound in terms $d$ for the number $(m-1)$-dimensional fibers $\phi$, using ideals minors Jacobian matrix. In particular, we answer affirmatively Question~11 arXiv:1511.02933v2.
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ژورنال
عنوان ژورنال: Journal of Algebra
سال: 2021
ISSN: ['1090-266X', '0021-8693']
DOI: https://doi.org/10.1016/j.jalgebra.2019.01.035