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Fibers of rational maps and Jacobian matrices
Journal of Algebra ( IF 0.8 ) Pub Date : 2021-04-01 , DOI: 10.1016/j.jalgebra.2019.01.035
Marc Chardin , Steven Dale Cutkosky , Quang Hoa Tran

Abstract A rational map ϕ : P k m ⇢ 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 ϕ, by using ideals of minors of the Jacobian matrix. In particular, we answer affirmatively Question 11 in [9] .

中文翻译:

有理映射和雅可比矩阵的纤维

摘要 有理映射 ϕ : P km ⇢ P kn 由公次为 d 的齐次多项式定义。我们通过使用雅可比矩阵的次要理想为 ϕ 的 ( m - 1 ) 维纤维的数量建立了关于 d 的线性界限。特别是,我们在 [9] 中肯定地回答了问题 11。
更新日期:2021-04-01
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