Gorenstein stable surfaces with KX2=1 and pg>0

In this paper we consider Gorenstein stable surfaces with KX2=1 and positive geometric genus. Extending classical results, we show that such surfaces admit a simple description as weighted complete intersection. We exhibit a wealth of surfaces of all possible Kodaira dimensions that occur as normali...

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Bibliographic Details
Published in:Mathematische Nachrichten 2017-04, Vol.290 (5-6), p.794-814
Main Authors: Franciosi, Marco, Pardini, Rita, Rollenske, Sönke
Format: Article
Language:English
Subjects:
14J10
14J29
moduli space of stable surfaces
Stable Gorenstein surface
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Summary:In this paper we consider Gorenstein stable surfaces with KX2=1 and positive geometric genus. Extending classical results, we show that such surfaces admit a simple description as weighted complete intersection. We exhibit a wealth of surfaces of all possible Kodaira dimensions that occur as normalisations of Gorenstein stable surfaces with KX2=1; for pg=2 this leads to a rough stratification of the moduli space. Explicit non‐Gorenstein examples show that we need further techniques to understand all possible degenerations.
ISSN:0025-584X
1522-2616
DOI:10.1002/mana.201600090