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Every real algebraic variety determines a Voronoi decomposition of its ambient Euclidean space.
Each Voronoi cell is a convex semialgebraic set in the normal space of the variety at a point.
We compute the algebraic boundaries of these Voronoi cells. Using intersection theory, we give a
formula for the degrees of the algebraic boundaries of Voronoi cells of curves and surfaces. We
discuss an application to low-rank matrix approximation. This is joint work with Diego
Cifuentes, Kristian Ranestad, and Bernd Sturmfels.
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