Projective duality identifies the moduli spaces B-n and X(3, n) parametrizing linearly general configurations of n points in P-2 and n lines in the dual P-2, respectively. The space X(3, n) admits Kapranov's Chow quotient comp actification (X) over bar (3, n), studied also by Lafforgue, Hacking, Keel, Tevelev, and Alexeev, which gives an example of a KSBA moduli space of stable surfaces: it carries a family of certain reducible degenerations of P-2 with n "broken lines". Gerritzen and Piwek proposed a dual perspective, a compact moduli space parametrizing certain reducible degenerations of P-2 with n smooth points. We investigate the relation between these approaches, answering a question of Kapranov from 2003.
Schaffler, L., Tevelev, J. (2022). Compactifications of Moduli of Points and Lines in the Projective Plane. INTERNATIONAL MATHEMATICS RESEARCH NOTICES, 2022(21), 17000-17078 [10.1093/imrn/rnab200].