K_X^2 = 1$ 和 $χ(X) = 3$ 的 2-Gorenstein 稳定曲面

arXiv - MATH - Algebraic Geometry Pub Date : 2024-09-12 DOI:arxiv-2409.07854

Stephen Coughlan, Marco Franciosi, Rita Pardini, Sönke Rollenske

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引用次数: 0

摘要

在稳定曲面的模空间中，$K_X^2 =1$和$\chi(X)=3$的一般类型曲面的Gieseker模空间的$overline M_{1,3}$紧凑化产生了所谓的稳定I型曲面。我们利用代数与几何混合技术，将所有这类 2 戈伦斯坦曲面分为四种类型。我们在 Gieseker 分量的闭合中发现了一个新的除数，并在模空间中发现了一个新的不可还原分量。

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

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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arXiv - MATH - Algebraic Geometry

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