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arXiv · 2409.07854

2-Gorenstein stable surfaces with $K_X^2 = 1$ and $\chi(X) = 3$

Stephen Coughlan·Marco Franciosi·Rita Pardini·Sönke Rollenske
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Abstract

The compactification $\overline M_{1,3}$ of the Gieseker moduli space of surfaces of general type with $K_X^2 =1 $ and $\chi(X)=3$ in the moduli space of stable surfaces parametrises so-called stable I-surfaces. We classify all such surfaces which are 2-Gorenstein into four types using a mix of algebraic and geometric techniques. We find a new divisor in the closure of the Gieseker component and a new irreducible component of the moduli space.

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Stephen Coughlan, Marco Franciosi, Rita Pardini, Sönke Rollenske. 2024-09-12. 2-Gorenstein stable surfaces with $K_X^2 = 1$ and $\chi(X) = 3$. https://arxiv.org/abs/2409.07854

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