Chow–Lam recovery equality for Plücker-linearly defined subvarieties
Prove that a subvariety V of Gr_C(k,n) defined by k(n−r)+1 generic linear Plücker equations coincides with its Chow–Lam recovery W_V (Conjecture 6.6).
References
Let $\mathcal{V}$ be a subvariety of the Grassmannian ${\rm Gr}\mathbb{C}(k,n)$ which is defined by $k(n-r)+1$ generic linear forms in the Pl\"ucker coordinates. Prove that $\mathcal{V}$ coincides with its Chow-Lam recovery $\mathcal{W}\mathcal{V}$. \hfill Conjecture 6.6.
— What is Positive Geometry?
(Ranestad et al., 18 Feb 2025) in Section “Open questions”: Problem [Pratt]