2-Gorenstein stable surfaces with $K_X^2 = 1$ and $χ(X) = 3$
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866913498556006400 |
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| author | Coughlan, Stephen Franciosi, Marco Pardini, Rita Rollenske, Sönke |
| author_facet | Coughlan, Stephen Franciosi, Marco Pardini, Rita Rollenske, Sönke |
| contents | The compactification $\overline M_{1,3}$ of the Gieseker moduli space of surfaces of general type with $K_X^2 =1 $ and $χ(X)=3$ 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_07854 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | 2-Gorenstein stable surfaces with $K_X^2 = 1$ and $χ(X) = 3$ Coughlan, Stephen Franciosi, Marco Pardini, Rita Rollenske, Sönke Algebraic Geometry The compactification $\overline M_{1,3}$ of the Gieseker moduli space of surfaces of general type with $K_X^2 =1 $ and $χ(X)=3$ 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. |
| title | 2-Gorenstein stable surfaces with $K_X^2 = 1$ and $χ(X) = 3$ |
| topic | Algebraic Geometry |
| url | https://arxiv.org/abs/2409.07854 |