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arXiv · 2607.19348

Degenerations of the complex projective plane with only rational singularities

Marcos Canedo·Giancarlo Urzúa
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Abstract

Wahl's conjecture states that two-dimensional singularities admitting a rational homology disk smoothing are weighted homogeneous. Assuming the conjecture, we classify all normal degenerations of the complex projective plane with only rational singularities. They are precisely the surfaces classified by Manetti and Hacking--Prokhorov, which are controlled by the Markov equation, together with six new degenerations containing four non-log canonical singularities.

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Marcos Canedo, Giancarlo Urzúa. 2026-07-21. Degenerations of the complex projective plane with only rational singularities. https://arxiv.org/abs/2607.19348

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