2017/06/26 by Blasco, Angel, Pérez-Díaz, Sonia
#Algebraic Geometry (math.AG) #FOS: Mathematics
paper · doi:10.48550/arxiv.1706.08430
Let \cal C be an algebraic space curve defined parametrically by \cal P(t)∈ \Bbb K(t)n, n≥ 2. In this paper, we introduce a polynomial, the T--function, T(s), which is defined by means of a univariate resultant constructed from \cal P(t). We show that T(s)=∏i=1n HPi(s)mi-1, where HPi(s), i=1,…,n are polynomials (called the fibre functions) whose roots are the fibre of the ordinary singularities Pi∈ \cal C of multiplicity mi, i=1,…,n. Thus, a complete classification of the singularities of a given space curve, via the factorization of a resultant, is obtained.