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Equivariant smoothing of cusp singularities

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arxiv 2302.00637 v3 pith:NVJCTXWI submitted 2023-02-01 math.AG math.SG

Yunfeng Jiang This is my paper · ORCID
classification math.AGmath.SG
keywords smoothingcuspequivariantsingularitiesadmitsalwayscompleteconjecture
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abstract

We generalize Looijenga's conjecture for smoothing surface cusp singularities to the equivariant setting. Moreover, we prove that for any cusp singularity which admits a one-parameter smoothing, the smoothing can always be induced by smoothing of locally complete intersection cusps. The result provides evidence for the existence of the moduli stack of $\lci$ covers over semi-log-canonical surfaces.

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Cited by 1 Pith paper

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  1. 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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