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arXiv · 2607.06686

The Algebraic Montgomery-Yang Problem

Woohyeok Jo·Jongil Park·Kyungbae Park
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Abstract

We completely resolve the algebraic Montgomery - Yang problem, a conjecture of Kollar stating that every rational homology projective plane with quotient singularities and a simply-connected smooth locus has at most three singular points. The crux of our proof is a new lattice theoretic constraint, obtained by combining Donaldson's diagonalization theorem with the distinguished spin^c structure on the smooth locus whose determinant line bundle is the canonical bundle. Together with the orbifold Bogomolov - Miyaoka - Yau inequality, this constraint rules out all remaining cases in the problem and completes the proof.

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Woohyeok Jo, Jongil Park, Kyungbae Park. 2026-07-07. The Algebraic Montgomery-Yang Problem. https://arxiv.org/abs/2607.06686

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