Deformations of complements of lines in \({\mathbb{P}}^ 2\) (Q1071075)
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scientific article; zbMATH DE number 3937314
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Deformations of complements of lines in \({\mathbb{P}}^ 2\) |
scientific article; zbMATH DE number 3937314 |
Statements
Deformations of complements of lines in \({\mathbb{P}}^ 2\) (English)
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1983
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We shall study deformations of complements of lines in \({\mathbb{P}}^ 2\), based on the theory of logarithmic deformation introduced by \textit{Y. Kawamata} [Math. Ann. 235, 247-264 (1978; Zbl 0363.32015)]. The result is that the standard completion of complements of lines in \({\mathbb{P}}^ 2\) has smooth versal family of logarithmic deformations. This provides examples of surfaces of logarithmic general type with unobstructed deformations even though \(H^ 2(X,\theta (\log D))\neq 0\).
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completion of complements of lines
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logarithmic deformations
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