  Let M be a smooth complex projective variety, bearing a K\"ahler symplectic
form \omega and a Hamiltonian action of a torus T, with finitely many fixed
points M^T. One standard form of the Duistermaat-Heckman theorem gives a
formula for M's Duistermaat-Heckman measure DH_T(M,\omega) as an alternating
sum of projections of cones, with overall direction determined by a Morse
decomposition of M.
  Using Victor Ginzburg's construction of Chern-Schwartz-MacPherson classes, we
show that these individual cone terms can themselves be interpreted as
Duistermaat-Heckman measures of cycles in T^*M. (This has a similar goal to the
symplectic cobordism approach of Viktor Ginzburg, Guillemin, and Karshon.) Our
approach also suggests extensions of the formula, including the Brianchon-Gram
theorem.
