Puiseux Expansions and Nonisolated Points in Algebraic Varieties. Issue 5 (3rd May 2016)

• Record Type: Journal Article
• Authors: Herrero, María Isabel; Jeronimo, Gabriela; Sabia, Juan
• Is Part Of: Communications in algebra. Volume 44:Issue 5(2016)
• Page Start: 2100
• Page End: 2109
• Publication Date: 2016-05-03
• Subjects: Algebraic varieties -- Curves -- Isolated points -- Puiseux series; 14Q05 -- 14Q20; Algebra -- Periodicals; 512.005
• DOI: 10.1080/00927872.2015.1033717
• Languages: English
• ISSNs: 0092-7872

Abstract

Abstract : 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.