Scheme structure in weak CHY formulation via reciprocal varieties

Determine the scheme structure of the intersection arising from the weak formulation of the CHY scattering equations, specifically the intersection of the reciprocal variety of the moduli space M_{0,n} with a linear space, as conjectured by Betti–Borovik–Telen (Conjecture 5.6).

Background

A weak formulation of CHY scattering equations leads to algebro-geometric intersections involving reciprocal varieties of M_{0,n}. Understanding the scheme structure (including multiplicities and embedded components) is necessary to rigorously connect algebraic geometry with the analytic CHY framework. This question refines the geometric underpinnings of scattering equations beyond point-set topology.