Complete collineations revisited

摘要: The space of complete collineations is a compactification the matrices fixed dimension and rank, whose boundary divisor with normal crossings. It was introduced in 19th century has been used to solve many enumerative problems. We show that this venerable can be understood using latest quotient constructions algebraic geometry. Indeed, there detailed analogy between moduli stable pointed curves genus zero. remarkable results Kapranov exhibiting latter as Chow quotient, Hilbert so on, all have counterparts for collineations. This encompasses Vainsencher's construction collineations, well form Gel'fand-MacPherson correspondence. There also tangential relation Gromov-Witten invariants Grassmannians. symmetric anti-symmetric versions problem are considered well. An appendix explains original motivation, which came from broken Morse flows moment map circle action.