Gorenstein stable Godeaux surfaces

Abstract

We classify Gorenstein stable numerical Godeaux surfaces with worse than canonical singularities and compute their fundamental groups.

Log-canonical pairs and Gorenstein stable surfaces with

“…Using this result, one can show that all the possible Kodaira dimensions occur in the normal case (cf. [FPR15b] and [FPR15a]), thus answering a question posed by Kollár during his lecture at the conference on 'Compact moduli and vector bundles' held at the University of Georgia in October 2010.…”

“…One can show that all the cases actually occur (see [FPR15b,FPR15a]). The proof of Theorem 4.1 occupies the rest of this section.…”

Marked Godeaux surfaces with special bicanonical fibers

“…We call these components of the solution space Ghost components. Perhaps these are stable Godeaux surfaces in the sense of [FPR18].…”

On T-divisors and intersections in $\overline{M}_{1,3}$

“…with canonical singularities, or more generally I-surfaces with K X Cartier, are very well understood. They are double covers of the quadric cone in P 3 branched over a quintic section and the vertex [FPR17]. Nonetheless, progress on understanding their degenerations, or better all I-surfaces has been slow.…”