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Singularity of Monomial Curves in A3 and Gorenstein Monomial Curves in A4

Published online by Cambridge University Press:  20 November 2018

Jürgen Kraft
Jürgen Kraft*
Affiliation:
University of Puerto Rico, May aguez, Puerto Rico
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Let 2 ≦ s ∊ N and {n1, …, ns) ⊆ N*. In 1884, J. Sylvester [13] published the following well-known result on the singularity degree S of the monomial curve whose corresponding semigroup is S: = 〈n1, …, ns): If s = 2, then

Let K: = –Z\S and

for all 1 ≦ i ≦ s. We introduce the invariant

of S involving a correction term to the Milnor number 2δ [4] of S. As a modified version and extension of Sylvester's result to all monomial space curves, we prove the following theorem: If s = 3, then

We prove similar formulas for s = 4 if S is symmetric.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 37 , Issue 5 , 01 October 1985 , pp. 872 - 892
Copyright
Copyright © Canadian Mathematical Society 1985

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