1988
DOI: 10.1090/s0273-0979-1988-15695-9
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Topological types and multiplicities of isolated quasi-homogeneous surface singularities

Abstract: ABSTRACT. TWO germs of 2-dimensional isolated quasi-homogeneous hypersurface singularities have the same topological type if and only if they have the same characteristic polynomial and the same fundamental group for their links. In particular, multiplicity is an invariant of topological type, an affirmative answer to Zariski's question in this case.Let (V, 0) and (W, 0) be germs of isolated hypersurface singularities in C n+1 . We say that (V, 0) and (W,0) have the same topological type if there is a germ of … Show more

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Cited by 13 publications
(6 citation statements)
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“…That is, L 0 (f ) depends only on the weights w i and the degree d in this case. Therefore it is concluded that L 0 (f ) is a topological invariant of f , by virtue of the results of Saeki [15] and Yau [20]. In view of the above equality it is reasonable to conjecture that the analogous result holds in general, that is, if f : (C n , 0) → (C, 0) is a weighted homogeneous polynomial, or even a semi-weighted homogeneous function (see Definition 4.1), with respect to (w 1 , .…”
Section: Introductionmentioning
confidence: 67%
“…That is, L 0 (f ) depends only on the weights w i and the degree d in this case. Therefore it is concluded that L 0 (f ) is a topological invariant of f , by virtue of the results of Saeki [15] and Yau [20]. In view of the above equality it is reasonable to conjecture that the analogous result holds in general, that is, if f : (C n , 0) → (C, 0) is a weighted homogeneous polynomial, or even a semi-weighted homogeneous function (see Definition 4.1), with respect to (w 1 , .…”
Section: Introductionmentioning
confidence: 67%
“…This difficulty is overcomed thanks to the Lojasiewicz's theory of relatively semi-algebraic, semi-analytic sets [27]. Thom [31], [33], [36], [37] [20], [21] [8], [7], [9]. Instead [16], [3].…”
mentioning
confidence: 99%
“…We remark that when d 2w i , for all i = 1, 2, 3, then L 0 (∇f ) = d−w 0 w 0 . As a consequence of (3) we have that if f : C 3 → C is a weighted homogeneous function with respect to (w 1 , w 2 , w 3 ), then L 0 (∇f ) is a topological invariant of f , by the results of Saeki [27] and Yau [32].…”
Section: Introductionmentioning
confidence: 82%