Desargues configurations via polar conics of plane cubics (Q2503114)

A Desargues configuration is the configuration of 10 points and 10 lines of the classical theorem of Desargues in the complex projective plane. Let \(M_D\) denote the (coarse) moduli space of Desargues configurations, and let \({\mathcal M}_6^b\) denote the moduli space of stable binary sextics. The authors showed in [Adv. Geom. 2, No. 3, 259--280 (2002; Zbl 1059.14064)] that there is a injective birational map \(\Phi_s\colon{\mathcal M}_D\rightarrow {\mathcal M}^b_6\), called Stephanos' map. In the paper under review, the authors study the inverse map \(\Phi_s^{-1}\); their main result states that this map concides with Marr's map [see \textit{W. L. Marr}, J. L. M. S. 1, 86--93 (1926; JFM 52.0655.04) and J. L. M. S. 5, 193-195 (1930; JFM 56.1164.04)], which is then, in particular, birational.