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arXiv · 2503.17563

Logarithmic Fulton--MacPherson configuration spaces

Siao Chi Mok
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Abstract

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.

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Siao Chi Mok. 2025-03-21. Logarithmic Fulton--MacPherson configuration spaces. https://arxiv.org/abs/2503.17563

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