An arrangement of hypersurfaces in projective space is SNC if and only if its Euler discriminant is nonzero. We study the critical loci of all Laurent monomials in the equations of the smooth hypersurfaces. These loci form 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 bihomogeneous prime ideal of this variety.

翻译：当且仅当其欧拉判别式非零时，射影空间中的超曲面构型为简单正规交叉（SNC）。我们研究了光滑超曲面方程中所有洛朗单项式的临界轨迹。这些轨迹在两个射影空间的乘积中构成一个不可约簇，在代数统计中称为似然对应，在粒子物理中称为散射对应。我们为该簇的双齐次素理想建立了一个显式的行列式表示。