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Scheme structure of weak CHY intersection

Determine the scheme structure of the intersection arising from the weak formulation of CHY scattering equations, namely the intersection of the reciprocal variety of M_{0,n} with a linear space.

References

A weak formulation of the CHY scattering equations leads to the intersection of the reciprocal variety of the moduli space $\mathcal{M}_{0,n}$ with a linear space. Determine the scheme structure of this intersection Conjecture~5.6.

What is Positive Geometry? (Ranestad et al., 18 Feb 2025) in Section “Open questions”: Problem [Betti]