2017/06/28 by Blasco, Angel, Pérez-Díaz, Sonia
#Algebraic Geometry (math.AG) #FOS: Mathematics
paper · doi:10.48550/arxiv.1706.09291
Let \cal P(t)∈ \Bbb K(t)n be a rational parametrization of an algebraic space curve \cal C. In this paper, we introduce the notion of limit point, PL, of the given parametrization P(t), and some remarkable properties of PL are obtained. In addition, we generalize the results in \citeMyB-2017 concerning the T--function, T(s), which is defined by means of a univariate resultant. More precisely, independently on whether the limit point is regular or not, we show that T(s)=∏i=1n HPi(s)mi-1. The polynomials HPi(s), i=1,…,n are the fibre functions, and its 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.