Godeaux surfaces with an Enriques involution and some stable degenerations

Margarida Mendes Lopes; Rita Pardini

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arXiv · 1502.04621

Godeaux surfaces with an Enriques involution and some stable degenerations

Margarida Mendes Lopes·Rita Pardini

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Abstract

We give an explicit description of the Godeaux surfaces that admit an involution such that the quotient surface is birational to an Enriques surface; these surfaces give a 6-dimensional unirational irreducible subset of the moduli space of surfaces of general type. In addition, we describe the Enriques surfaces that are birational to the quotient of a Godeaux surface by an involution and we show that they give a 5-dimensional unirational irreducible subset of the moduli space of Enriques surfaces. Finally, by degenerating our description we obtain some examples of non-normal stable Godeaux surfaces.

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BibTeX RIS

Margarida Mendes Lopes, Rita Pardini. 2015-02-16. Godeaux surfaces with an Enriques involution and some stable degenerations. https://arxiv.org/abs/1502.04621

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