Moment Varieties of Measures on Polytopes

Understand

The uniform probability measure on a convex polytope induces piecewise polynomial densities on its projections.

• For a fixed combinatorial type of simplicial polytopes, the moments of these measures are rational functions in the vertex coordinates.
• We study projective varieties that are parametrized by finite collections of such rational functions.
• Our focus lies on determining the prime ideals of these moment varieties.