Smooth Realizations of Line Configurations

Paolo Aceto; Duncan McCoy; JungHwan Park

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arXiv · 2607.09439

Smooth Realizations of Line Configurations

Paolo Aceto·Duncan McCoy·JungHwan Park

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Abstract

We study the problem of realizing line configurations as collections of 2-spheres smoothly embedded in the complex projective plane. Building upon prior work by Ruberman and Starkston on topological realizations, we establish a stronger obstruction in the smooth category. Our proof relies on lattice-theoretic arguments based on Donaldson's diagonalization theorem.

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Paolo Aceto, Duncan McCoy, JungHwan Park. 2026-07-10. Smooth Realizations of Line Configurations. https://arxiv.org/abs/2607.09439

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