  The so-called Scattering Equations which govern the kinematics of the
scattering of massless particles in arbitrary dimensions have recently been
cast into a system of homogeneous polynomials. We study these as affine and
projective geometries which we call Scattering Varieties by analyzing such
properties as Hilbert series, Euler characteristic and singularities.
Interestingly, we find structures such as affine Calabi-Yau threefolds as well
as singular K3 and Fano varieties.
