Suppose G acts on a variety X. A fundamental problem in geometric invariant theory is to determine the closed orbits of G in X. These orbits correspond to the points in the quotient variety \(X/\mkern -5mu/ G\) , so this is the first step towards understanding the geometry of the quotient. Often it is of particular interest to find an open dense set of points on which the quotient map \(\pi \colon X\to X/\mkern -5mu/ G\) is especially well-behaved. Moreover, once the closed orbits are known, one can study degeneration phenomena: the way in which a point in a non-closed orbit can be brought inside a closed orbit by taking a limit along a cocharacter.