Maximum likelihood duality for determinantal varieties (Q2929655)

\textit{J. Hauenstein}, \textit{J. Rodriguez} and \textit{B. Sturmfels} [``Maximum likelihood for matrices with rank constraints'', preprint, \url{arXiv:1210.0198}] conjectured a bijection between critical points of the likelihood functions on the complex varieties defined by certain matrices. The authors prove this conjecture for two cases: rectangular matrices and symmetric matrices, respectively. Furthermore, they prove a variant for skew-symmetric matrices. In all three cases, they provide an explicit construction of the bijection. The strategy of proof is always the same, but there are sufficiently many differences so that all three results must be proven separately.