Timeline for Classification of "extensions" of algebraic varieties
Current License: CC BY-SA 4.0
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| Jan 5, 2020 at 4:18 | history | edited | Zhiyu | CC BY-SA 4.0 |
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| Jan 5, 2020 at 3:00 | comment | added | pinaki | In another words you are asking about classifications of "projective compactifications'' of $U$. It is not even known for your second example $Z = \mathbb{P}^{n-1}$, $U = \mathbb{A}^n$. For this example the complete answer for $n = 2$ and $k = \mathbb{C}$ can be found from this paper of mine: arxiv.org/abs/1307.5577 (combine Proposition 3.3 and Corollary 3.5). In particular there are examples other than $X = \mathbb{P}^2$, e.g. the weighted projective surfaces of the form $\mathbb{P}^2(1,p,q)$. | |
| Jan 5, 2020 at 1:36 | history | asked | Zhiyu | CC BY-SA 4.0 |