On local real algebraic geometry and applications to kinematics

2019/07/28 by Diesse, Marc
#Algebraic Geometry (math.AG) #Commutative Algebra (math.AC) #FOS: Computer and information sciences #FOS: Mathematics #Robotics (cs.RO)

paper · doi:10.48550/arxiv.1907.12134

Abstract

We address the question of identifying non-smooth points in affine real algebraic varieties. A simple algebraic criterion will be formulated and proven. As an application we can answer several questions about the configuration spaces of some class of planar linkages.

Related

• Smooth connectivity in real algebraic varieties
• Explicit smooth real algebraic functions which may have both compact and non-compact preimages on smooth real algebraic manifolds
• Universality theorems for configuration spaces of planar linkages
• Geometric models for algebraic suspensions
• Smooth maps to the plane and Pontryagin classes, Part I: Local aspects