The Picard group of the variety of plane cuspidal cubics of \(\mathbb{P}^3\) (Q1567575)
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scientific article; zbMATH DE number 1462206
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | The Picard group of the variety of plane cuspidal cubics of \(\mathbb{P}^3\) |
scientific article; zbMATH DE number 1462206 |
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The Picard group of the variety of plane cuspidal cubics of \(\mathbb{P}^3\) (English)
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4 September 2000
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Consider the family \(M\) of nondegenerate plane cuspidal cubics in \({\mathbb{P}^3}\). A compactification \(\bar{M}\) can be constructed as the projectivization \(\bar{M}=\mathbb{P}({\mathcal E})\) of a suitable vector bundle \({\mathcal E}\). The author constructs a resolution of \(\bar{M}\) and uses this to compute the Chow ring \(\text{CH}(\bar{M})\) (and hence, in particular, the Picard group \(\text{Pic}(\bar{M})\)).
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