Encomplexing the writhe

Abstract

A detailed version of preprint "Self-linking number of a real algebraic link" by the same author, alg-geom/9410030. For a nonsingular real algebraic curve in 3-dimensional projective space or 3-sphere, a new integer-valued characteristic is introduced. It is invariant under rigid isotopy and multiplied by -1 under mirror reflections. In a sense, it is a Vassiliev invariant of degree 1 and a counterpart of a link diagram writhe. For a regular complete intersection this invariant vanishes, while for rational knots of degree d it takes all the values between -(d-1)(d-2)/2 and (d-1)(d-2)/2.