# Constructing $T$-singular surfaces – Julie Rana (Lawrence University)

#### Venue

Dipartimento di Matematica, Aula Magna.

#### Abstract

Semi-log-canonical surfaces with ample canonical divisors are called stable. Their moduli space is a natural compactification (the KSBA compactification) of the Gieseker moduli space of canonical models of surfaces of general type. Among the singularities that are allowed in stable surfaces, we have cyclic quotient singularities $1/m(1; q)$, and a special role is played by those with $m =dn^2$, $q=dna-1$ $\mathsf{gcd}(n; a) = 1$. These singularities together with all du Val singularities are called T-singularities. We give bounds on such singularities and describe some constructions.

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