Algebraic C*-actions and the inverse kinematics of a general 6R manipulator

Let X be a smooth quadric of dimension 2m in P C and let Y, Z ⊂ X be subvarieties both of dimension m which intersect transversely. In this paper we give an algorithm for computing the intersection points of Y ∩ Z based on a homotopy method. The homotopy is constructed using a C∗-action on X whose fixed points are isolated, which induces Bialynicki-Birula decompositions of X into locally closed invariant subsets. As an application we present a new solution to the inverse kinematics problem of a general sixrevolute serial-link manipulator.