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.
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页码：40 / 54
页数：15
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