In Kapranov's marvelous paper Chow quotients of Grassmannian I, he proves that $\overline{M}_{0,n}$ is isomorphic to both the Hilbert quotient and Chow quotient $(\mathbb{P}^1)^n//\text{SL}_2$. These quotients are by definition closed subvarieties of the Hilbert scheme and Chow variety (respectively) of $(\mathbb{P}^1)^n$. Every Chow variety has a natural polarization coming from Chow forms, and Hilbert schemes have a family of polarizations. Is it known what ample divisors on $\overline{M}_{0,n}$ we get by restricting these polarizations via Kapranov's construction?
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