Generalized polar varieties and an efficient real elimination procedure (original) (raw)

This paper introduces the concept of generalized polar varieties associated with a pure p-codimensional closed algebraic subvariety in projective space, considering specific linear subspaces, hyperquadrics, and hyperplanes. Two instances of generalized polar varieties are explored: direct polar varieties, which are classic, and dual polar varieties that offer non-classical insights. The discussion extends to the affine traces of these varieties, characterized as conic and cylindric polar varieties, leading to applications and implications for geometric understanding and elimination algorithms.