Smooth Realizations of Line Configurations

Paolo Aceto; Duncan McCoy; JungHwan Park

Smooth Realizations of Line Configurations

Geometric Topology 2026-07-10 v1 Algebraic Geometry Combinatorics

Authors: Paolo Aceto , Duncan McCoy , JungHwan Park

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.

Keywords

line configurations smooth realizations complex projective plane Donaldson's diagonalization theorem lattice-theoretic arguments

Cite

@article{arxiv.2607.09439,
  title  = {Smooth Realizations of Line Configurations},
  author = {Paolo Aceto and Duncan McCoy and JungHwan Park},
  journal= {arXiv preprint arXiv:2607.09439},
  year   = {2026}
}

Comments

18 pages. Comments are welcome