The Likelihood Correspondence

Abstract

An arrangement of hypersurfaces in projective space is strict normal crossing (SNC) if and only if its Euler discriminant is nonzero. We study the critical loci of arbitrary Laurent monomials in the equations of the smooth hypersurfaces. The family of these loci forms an irreducible variety in the product of two projective spaces, known in algebraic statistics as the likelihood correspondence and in particle physics as the scattering correspondence. We establish an explicit determinantal representation for the minimal generators of the bihomogeneous prime ideal that defines this variety.