Polar Varieties: History and Introduction

Time: 9:30 - 10h30, 7th September

Venue: Room 507, A6, Institute of Mathematics

Abstract: The history of Polar Varieties starts with Blaise Pascal (1623-1662) and his work on conics. Then Jean-Victor Poncelet (1788-1867) introduced the notion of duality by poles and polars, or polar transformation. Examples of polar transformation in Euclidean space R^3 gives the idea of polar variety.

The generalisation by Francesco Severi (1879-1961) and John Arthur Todd (1908-1994) led to the relationship between polar varieties and characteristic classes of smooth manifolds. More recently Lê Dung Trang and Bernard Teissier define polar varieties for singular varieties and the relation with the characteristic classes of singular varieties, as defined by Marie-Hélène Schwartz and Robert MacPherson.