Title: Logarithmic Fulton—MacPherson configuration spaces
Abstract: The Fulton—MacPherson configuration space is a well-known compactification of the ordered configuration space of a projective variety. We describe a construction of its logarithmic analogue: it is a compactification of the configuration space of points on a projective variety X away from a simple normal crossings divisor D, and is constructed via logarithmic and tropical geometry. Moreover, given a semistable degeneration of X, we construct a logarithmically smooth degeneration of the Fulton—MacPherson space of X. 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. Time permitting, we explore some potential applications to enumerative geometry.