Sulla trasversalità di due superfici in $\mathbf{P}^{3}$

Giuffrida, Salvatore

Atti della Accademia nazionale dei Lincei. Rendiconti della Classe di scienze fisiche, matematiche e naturali, Série 8, Tome 81 (1987) no. 2, pp. 119-123

Résumé

Let $C \in \mathbf{P}^{3}$ be a reduced and irreducible curve, and $I(C) = f_{1},f_{2},...,f_{m}$ be the homogeneous ideal of $C$, where $f_{1},f_{2},...,f_{m}$ are a minimal system of generators for $I(C)$. In § 2 we find a necessary and sufficient condition in order that two surfaces $F_{i}$, $F_{j}$, having equations $f_{i} = 0$, $f_{j} = 0$$(i,j = 1,2,...,m)$, intersect transversally along $C$. In § 3 we give an application of this result to arithmetically Cohen-Macaulay curves.