Puiseux expansions and non-isolated points in algebraic varieties

HERRERO, MARÍA ISABEL; JERONIMO, GABRIELA; SABIA, JUAN

COMMUNICATIONS IN ALGEBRA

TAYLOR & FRANCIS INC

Lugar: Philadelphia; Año: 2016 vol. 44 p. 2100 - 2109

0092-7872

We consider the problem of deciding whether a common solution to a multivariate polynomial equation system is  isolated or not. We present conditions on a given truncated Puiseux series vector centered at the point ensuring that it is not isolated. In addition, in the case that the set of all common solutions of the system has dimension 1, we obtain further conditions specifying to what extent the given vector of truncated Puiseux series coincides with the initial part of a parametrization of a curve of solutions passing through the point.