Abstract
Abstract We construct examples of non-smoothable stable surface with invariants in a wide range comprising all possible invariants of smooth minimal surfaces of general type but non-standard second plurigenus. We deduce that the moduli space of stable surfaces $\overline {{\mathfrak {M}}}_{k,l}$ has at least $k-l+2$ connected components distinguished by the second plurigenus and, in particular, always has more irreducible components than the Gieseker moduli space with the same invariants.
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