  We study the projective properties of planar zeros of tree-level scattering
amplitudes in various theories. Whereas for pure scalar field theories we find
that the planar zeros of the five-point amplitude do not enjoy projective
invariance, coupling scalars to gauge fields gives rise to tree-level
amplitudes whose planar zeros are determined by homogeneous polynomials in the
stereographic coordinates labelling the direction of flight of the outgoing
particles. In the case of pure gauge theories, this projective structure is
generically destroyed if string corrections are taken into account. Scattering
amplitudes of two scalars with graviton emission vanish exactly in the planar
limit, whereas planar graviton amplitudes are zero for helicity violating
configurations. These results are corrected by string effects, computed using
the single-valued projection, which render the planar amplitude nonzero.
Finally, we discuss how the structure of planar zeros can be derived from the
soft limit behavior of the scattering amplitudes.
