Equivariant smoothing of cusp singularities

2023/02/01 by Jiang, Yunfeng · 1 citation
#Algebraic Geometry (math.AG) #FOS: Mathematics #Symplectic Geometry (math.SG)

paper · doi:10.48550/arxiv.2302.00637

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.

Cited by

• Equivariant deformation of minimally elliptic singularities

Related

• Smoothing of surface singularities via equivariant smoothing of lci covers
• ℤ/2ℤ-Equivariant smoothings of cusp singularities
• Durfee's conjecture on the signature of smoothings of surface singularities
• Equivariant deformation of minimally elliptic singularities
• Motivic Poincaré series of cusp surface singularities