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arXiv · 2302.00637

Equivariant smoothing of cusp singularities

Yunfeng Jiang
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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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Yunfeng Jiang. 2023-02-01. Equivariant smoothing of cusp singularities. https://arxiv.org/abs/2302.00637

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