Some remarks concerning Voevodsky’s nilpotence conjecture

In this article we extend Voevodsky’s nilpotence conjecture from smooth projective schemes to the broader setting of smooth proper dg categories. Making use of this noncommutative generalization, we then address Voevodsky’s original conjecture in the following cases: quadric fibrations, intersection of quadrics, linear sections of Grassmannians, linear sections of determinantal varieties, homological projective duals, and Moishezon manifolds.

Singularity Variety of a 3SPS-1S Spherical Parallel Manipulator

In this paper, we study the manifold of configurations of a 3SPS-1S spherical parallel manipulator. This manifold is obtained as the intersection of quadrics in the hypersphere defined by quaternion coordinates and is called its constraint manifold. We then formulate Jacobian for this manipulator and consider its singular. This is a quartic algebraic manifold called the singularity variety of the parallel manipulator. A survey of the architectures that can be defined for the 3SPS-1S spherical parallel manipulators yield a number of special cases, in particular the architectures with coincident base or moving pivots yields singularity varieties that factor into two quadric surfaces.