ABSTRACT
Both Beppo Levi and Beniamino Segre made use of polar varieties of projective varieties in their studies of resolution of singularities of surfaces. Segre introduced the Segre classes, which are similar in spirit to the polar classes, replacing tangent spaces by secant lines, and provided numerical invariants of embeddings. This chapter recalls the more modern definition of local polar varieties and draws attention by examples to the importance of the geometric viewpoint in the theory of polar varieties. It also provides a discussion on the contact of polar varieties and resolution of singularities.
