Bidegree (2,1) parametrizable surfaces in projective 3-space

The main purpose of this paper is to study projective classes of bidegree (2,1) parametrizable surfaces in a real projective 3-space. It turns out that the implicit degree of such surfaces is two, three, or four, and singular curves have degree three. We describe all possibilities for singular curves and pinch points on such surfaces. The presentation has been made from the point of view of analytic geometry and does not presume a deep knowledge of algebraic geometry. Partially supported by the Lithuanian State Science and Studies Foundation. Vilnius University, Naugarduko 24, 2006 Vilnius, Lithuania. Published in Lietuvos Matematikos Rinkinys, Vol. 38, No. 3, pp. 379–402, July–September, 1998.