  We show that the maximum likelihood degree of a smooth very affine variety is
equal to the signed topological Euler characteristic. This generalizes Orlik
and Terao's solution to Varchenko's conjecture on complements of hyperplane
arrangements to smooth very affine varieties. For very affine varieties
satisfying a genericity condition at infinity, the result is further
strengthened to relate the variety of critical points to the
Chern-Schwartz-MacPherson class. The strengthened version recovers the
geometric deletion-restriction formula of Denham et al. for arrangement
complements, and generalizes Kouchnirenko's theorem on the Newton polytope for
nondegenerate hypersurfaces.
