In this talk I will describe the normal stable surfaces with K2=2pg−3 whose only non canonical singularity is a cyclic quotient singularity of type 14k(1,2k−1) and the corresponding locus DD inside the KSBA moduli space of stable surfaces. The main result is the following: for pg≥15, (1) a general point of any irreducible component of DD corresponds to a surface with a singularity of type 14(1,1), (2) the closure of DD is a divisor contained in the closure of the Gieseker moduli space of canonical models of surfaces with K2=2pg−3 and intersects all the components of such closure, and (3) the KSBA moduli space is smooth at a general point of DD. Moreover DD has 1 or 2 irreducible components, depending on the residue class of pgpg modulo 4. This is joint work with Rita Pardini.
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