Tags:Intersection theory, Isosingular sets, Numerical algebraic geometry, Numerical irreducible decomposition and Polynomial system
Abstract:
A fundamental problem in algebraic geometry is to decompose the solution set of a polynomial system. A numerical description of this solution set is called a numerical irreducible decomposition. Standard algorithms use a sequence of homotopies in a dimension-by-dimension approach. We provide a new approach by pairing a classical result that computes a smooth point on every irreducible component in every dimension using a single homotopy together with the theory of isosingular sets.
Excess Intersections and Numerical Irreducible Decompositions