# Automorphisms of numerical Godeaux surfaces with torsion of order 3, 4, or 5

@article{Maggiolo2010AutomorphismsON, title={Automorphisms of numerical Godeaux surfaces with torsion of order 3, 4, or 5}, author={Stefano Maggiolo}, journal={arXiv: Algebraic Geometry}, year={2010} }

We compute the automorphisms groups of all numerical Godeaux surfaces, i.e. minimal smooth surfaces of general type with K^2 = 1 and p_g = 0, with torsion of the Picard group of order \nu equals 3, 4, or 5. We present explicit stratifications of the moduli spaces whose strata correspond to different automorphisms groups.
Using the automorphisms computation, for each value of \nu we define a quotient stack, and prove that for \nu = 5 this is indeed the moduli stack of numerical Godeaux surfaces…

## 4 Citations

### Godeaux surfaces with an Enriques involution and some stable degenerations

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We give an explicit description of the Godeaux surfaces S (minimal surfaces of general type with \( K_{S}^{2} = \chi ({\mathcal{O}}_{S} ) = 1 \)) that admit an involution σ such that S/σ is…

### On the automorphism group of certain algebraic varieties

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### NOTES ON AUTOMORPHISMS OF SURFACES OF GENERAL TYPE WITH $p_{g}=0$ AND $K^{2}=7$

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