Geodesic
Singularity of Monomial Curves in A3 and Gorenstein Monomial Curves in A4
Canadian journal of mathematics, Tome 37 (1985) no. 5, pp. 872-892

Voir la notice de l'article provenant de la source Cambridge University Press

Let 2 ≦ s ∊ N and {n 1, ..., 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: = 〈n 1, ..., 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. 
Kraft, Jürgen. Singularity of Monomial Curves in A3 and Gorenstein Monomial Curves in A4. Canadian journal of mathematics, Tome 37 (1985) no. 5, pp. 872-892. doi: 10.4153/CJM-1985-047-8
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