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Discriminant of a Germ Φ: (C 2 , 0)→(C 2 , 0) and Seifert Fibred Manifolds
Author(s) -
Maugendre Hélène
Publication year - 1999
Publication title -
journal of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.441
H-Index - 62
eISSN - 1469-7750
pISSN - 0024-6107
DOI - 10.1112/s0024610798006887
Subject(s) - quotient , jacobian matrix and determinant , discriminant , fibered knot , order (exchange) , mathematics , germ , pure mathematics , combinatorics , physics , mathematical analysis , computer science , artificial intelligence , finance , economics
Let f and g be two analytic function germs without common branches. We define the Jacobian quotients of ( g , f ), which are ‘first order invariants’ of the discriminant curve of ( g , f ), and we prove that they only depend on the topological type of ( g , f ). We compute them with the help of the topology of ( g , f ). If g is a linear form transverse to f , the Jacobian quotients are exactly the polar quotients of f and we affirm the results of D. T. Lê, F. Michel and C. Weber.