Smoothing semi-smooth Stable Godeaux surfaces
Barbara Fantechi, Marco Franciosi, Rita Pardini
TL;DR
This paper proves that all semi-smooth stable complex Godeaux surfaces are smoothable and that their moduli stack is smooth with the expected dimension, advancing understanding of their deformation theory.
Contribution
It establishes the smoothability of semi-smooth stable Godeaux surfaces and confirms the smoothness and dimension of their moduli stack.
Findings
All semi-smooth stable Godeaux surfaces are smoothable.
The moduli stack is smooth of dimension 8 at the relevant points.
Provides a classification-based proof of smoothability.
Abstract
We show that all the semi-smooth stable complex Godeaux surfaces, classified in [FPR18a], are smoothable, and that the moduli stack is smooth of the expected dimension 8 at the corresponding points.
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Taxonomy
TopicsAlgebraic Geometry and Number Theory · Geometry and complex manifolds · Geometric and Algebraic Topology