chi F
By definition, the Euler characteristic of coherent sheaf $F$ on a variety $X$ is $\sum_i (1)^i$ dim $HH^i (X, F)$. However, this methods uses the HirzebruchRiemannRoch theorem to calculate the Euler characteristic.
For a nef line bundle on a normal toric variety, the Euler characteristic equals the number of lattice points in the corresponding polytope.






