Numerical irreducible decomposition of multiprojective varieties

Abstract

In the field of numerical algebraic geometry, positive-dimensional solution sets of systems of polynomial equations are described by witness sets. In this paper, we define multiprojective witness sets which will encode the multidegree information of an irreducible multiprojective variety. Furthermore, we generalize the regeneration solving procedure, a trace test, and numerical irreducible decomposition to the multiprojective case. Examples are included to demonstrate this new approach.