Fibers of rational maps and Jacobian matrices
Résumé
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.
Domaines
Algèbre commutative [math.AC]
Origine : Fichiers produits par l'(les) auteur(s)
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