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Optimal bounds for many T-singularities in stable surfaces

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arxiv 2308.05624 v2 pith:IPRLNV7C submitted 2023-08-10 math.AG math.GTmath.SG

Fernando Figueroa , Julie Rana , Giancarlo Urzúa This is my paper · ORCID
classification math.AGmath.GTmath.SG
keywords t-singularitiesboundboundscasecombinatorialconfigurationsoptimalsingularities
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We effectively bound T-singularities on non-rational projective surfaces with an arbitrary amount of T-singularities and ample canonical class. This fully generalizes the previous work for the case of one singularity, and illustrates the vast increase in combinatorial complexity as the number of singularities grows. We find that certain combinatorial configurations lead to relatively high bounds. We classify all such configurations, and show that their non-existence gives a strong and optimal bound. As an application, we work out in detail the case of two singularities.

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Cited by 2 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Degenerations of the complex projective plane with only rational singularities

    math.AG 2026-07 conditional novelty 7.0 of 10

    Assuming Wahl's conjecture, every normal degeneration of the projective plane to a surface with only rational singularities is one of the Markov-equation family or one of six newly found surfaces.

  2. Normal stable degenerations of Noether-Horikawa surfaces

    math.AG 2025-07 conditional novelty 7.0 of 10

    Every Q-Gorenstein smoothable normal stable Horikawa surface falls into one of seven explicit families, and its global smoothability is controlled by a single local condition at its elliptic double cone singularities.

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