Finite A-determinacy of generic homogeneous map germs in C-3

Author(s)

Farnik, Michal ^[1] ; Jelonek, Zbigniew ^[2] ; Soares Ruas, Maria Aparecida ^[3]

Affiliation

^[1] Jagiellonian Univ, Fac Math & Comp Sci, Lojasiewicza 6, PL-30348 Krakow - Poland

^[2] Polish Acad Sci, Inst Matemat, Sniadeckich 8, PL-00656 Warsaw - Poland

^[3] ICMC USP, Dept Matemat, Caixa Postal 668, BR-13560970 Sao Carlos, SP - Brazil

• Document type: Journal article
• Source: JOURNAL OF THE MATHEMATICAL SOCIETY OF JAPAN; v. 73, n. 1, p. 211-220, JAN 2021.
• Web of Science Citations: 0

Abstract

Denote by H(d(1), d(2), d(3)) the set of all homogeneous polyno- mial mappings F = f(1), f(2), .f(3)) : C-3 -> C-3, such that deg f(i) = d(i). We show that if gcd(d(i), d(j)) <= 2 for 1 <= i < j <= 3 and gcd(d(1), d(2), d(3)) = 1, then there is a non-empty Zariski open subset U subset of H(d(1),d(2), d(3)) such that for every mapping F is an element of U the map germ (F, 0) is A-finitely determined. Moreover, in this case we compute the number of discrete singularities (0-stable singularities) of a generic mapping (f(1), f(2), f(3)) : C-3 -> C-3, where deg f(i) = d(i). (AU)

• FAPESP's process: 14/00304-2 - Singularities of differentiable mappings: theory and applications
• Grantee: Maria Aparecida Soares Ruas
• Support Opportunities: Research Projects - Thematic Grants