The Convex Hull of a Variety

TL;DR

This paper characterizes the boundary hypersurfaces of the convex hull of a compact real algebraic variety using projective biduality, providing a geometric understanding of these boundaries.

Contribution

It introduces a novel characterization of boundary hypersurfaces of convex hulls in terms of projective biduality, linking convex geometry and algebraic geometry.

Findings

Boundary hypersurfaces characterized by projective biduality

Connection established between convex hull boundaries and algebraic geometry

Provides a new geometric perspective on convex hulls of algebraic varieties

Abstract

We present a characterization, in terms of projective biduality, for the hypersurfaces appearing in the boundary of the convex hull of a compact real algebraic variety.