Fibers of rational maps and Jacobian matrices

被引：0

作者：

Chardin, Marc ^{[1
]}

Cutkosky, Steven Dale ^{[2
]}

Quang Hoa Tran ^{[3
]}

机构：

[1] UPMC, Inst Math Jussieu, 4 Pl Jussieu, F-75005 Paris, France

[2] Univ Missouri, Dept Math, Columbia, MO 65211 USA

[3] Hue Univ, Univ Educ, 34 Le Loi St, Hue City, Vietnam

来源：

JOURNAL OF ALGEBRA | 2021年 / 571卷

关键词：

Rational maps; Tangent space; Fibers of rational maps; Jacobian matrices; Blow-up algebras;

D O I：

10.1016/j.jalgebra.2019.01.035

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

A rational map empty set : 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 empty set, by using ideals of minors of the Jacobian matrix. In particular, we answer affirmatively Question 11 in [9]. (C) 2019 Elsevier Inc. All rights reserved.

引用

页码：40 / 54

页数：15

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