Degree of rational maps versus syzygies

JOURNAL OF ALGEBRA

卷:573

Article

Chardin, M.^1,2  Hassanzadeh, S. H.³  Simis, A.⁴ 

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

[2] Sorbonne Univ, 4 Pl Jussieu, F-75005 Paris, France

[3] Univ Fed Rio de Janeiro, Ctr Tecnol, Bloco C,Sala ABC,Cidade Univ, BR-21941909 Rio De Janeiro, RJ, Brazil

[4] Univ Fed Pernambuco, Dept Matemat, CCEN, BR-50740560 Recife, PE, Brazil

关键词: Degree of rational maps;    Multiplicity;    Syzygy;    Rees algebra;    Symmetric algebra;    Jacobian dual rank;    Lower bound;    Upper bound;   

DOI  :  10.1016/j.jalgebra.2021.01.001

来源: Elsevier

【 摘 要 】

One proves a far-reaching upper bound for the degree of a generically finite rational map between projective varieties over a base field of arbitrary characteristic. The bound is expressed as a product of certain degrees that appear naturally by considering the Rees algebra (blowup) of the base ideal defining the map. Several special cases are obtained as consequences, some of which cover and extend previous results in the literature. (C) 2021 Elsevier Inc. All rights reserved.

【 授权许可】

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