The Scattering Variety

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.