Logarithmic Fulton--MacPherson configuration spaces

Using techniques in logarithmic geometry, we construct a logarithmic analogue of the Fulton–MacPherson configuration spaces. We similarly construct a logarithmically smooth degeneration of the Fulton–MacPherson configuration spaces. Both constructions parametrise point configurations on certain target degenerations arising from both logarithmic geometry and the original Fulton–MacPherson construction. The degeneration satisfies a “degeneration formula” – each irreducible component of its special fibre can be described as a proper birational modification of a product of logarithmic Fulton–MacPherson configuration spaces.