Toric amplitudes and universal adjoints

Abstract A toric amplitude is a rational function associated with a simplicial polyhedral fan. The definition is inspired by scattering amplitudes in particle physics. We prove algebraic properties of such amplitudes and study the geometry of their zero loci. These hypersurfaces play the role of Warren's adjoint via a dual volume interpretation. We investigate their Fano schemes and singular loci using the nef cone and toric irrelevant ideal of the fan.