Polydiagonal compactification of configuration spaces

A smooth compactification X <n > of the configuration space of it distinct labeled points in a smooth algebraic variety X is constructed by a natural sequence of blowups, with the full symmetry of the permutation group S mani fest at each stage. The strata of the normal crossing divisor at infinity a re labeled by leveled trees anti their structure is studied. This is the ma ximal wonderful compactification in the sense of De Concini-Procesi. and it has a strata-compatible surjection onto the Fulton MacPherson compactifica tion. The degenerate configurations added in the compactification are geome trically described by polyscreens similar to the screens of Fulton and MacP herson. In characteristic 0, isotropy subgroups of the action of S on X(n) are abel ian, thus X <n > may be a step toward an explicit resolution of singulariti es of the symmetric products X-n/S-n.