On the convex hull of a space curve (Q2891074)

This nicely written paper investigates the algebraic-geometric structure of the convex hull of a compact algebraic curve in real three-dimensional space. The authors describe practical tools (of computer algebra) to compute the polynomials defining the boundary surface, and bound their degrees, in terms of the degree, genus and singularities of the curve. They show that the boundary surface is an union of tritangent planes and an irreducible edge surface, itself an union of bisecant lines. Formulas are given for the degree of the edge surface and the number of tritangent planes, for smooth and singular curves. The paper contains many illustrating examples with explicit computations. These results have been extended by the authors to higher-dimensional varieties in [\textit{K. Ranestad} and \textit{B. Sturmfels}, in: Notions of positivity and the geometry of polynomials. Basel: Birkhäuser, 331--344 (2011; Zbl 1222.00033)].