Abstract:  It is well-known that semi-log-canonical (slc) singularities of log general type varieties are the worst singularities in the Koll\'ar-Shepherd-Barron-Alexeev (KSBA) compactification of moduli space of log general type varieties.  In the surface case, the slc singularities were classified.  Except the locally complete intersection (lci) singularities,  the only slc surface singularities in the index one cover of an slc surface  are simple elliptic singularities, cusp and degenerate cusp singularities.  The smoothing of such singularities had been studied for a long time. In this talk we study the equivariant smoothing of such singularities by lci covers, and classify when such singularities admit equivariant smoothing of the same type  lci singularities.  The study of the equivariant smoothing is motivated by the construction of virtual fundamental class on KSBA spaces.