Timeline for The fundamental group of a complex, quasi-affine variety
Current License: CC BY-SA 3.0
10 events
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| Sep 26, 2013 at 12:48 | history | edited | Francesco Polizzi | CC BY-SA 3.0 |
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| Sep 26, 2013 at 12:23 | history | edited | Francesco Polizzi | CC BY-SA 3.0 |
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| Sep 26, 2013 at 12:07 | comment | added | Francesco Polizzi | If $V$ is irreducible of degree $d$, in general the abelianization of $\pi_1(U)$ is $\mathbb{Z}/d \mathbb{Z}$. However, if $V$ is not normal crossing in codimension $1$, it may happen that $\pi_1(U)$ is not abelian. I added a couple of classical examples illustating this situation. | |
| Sep 25, 2013 at 14:43 | comment | added | user19475 | Perhaps by considering $\mathrm{Pic}(U) = \mathrm{Cl}(U)$ and $H^1(U,\mathbf{Z}(1))$. | |
| Sep 25, 2013 at 14:40 | comment | added | user19475 | Is there a connection between of $\mathrm{Cl}(U) = \mathbf{Z}/d$ and $\pi_1(U)$ as for $U = \mathbf{P}^n \setminus V$ in general? | |
| Sep 25, 2013 at 12:38 | history | edited | Francesco Polizzi | CC BY-SA 3.0 |
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| Sep 25, 2013 at 12:20 | vote | accept | IMeasy | ||
| Sep 25, 2013 at 12:19 | history | edited | Francesco Polizzi | CC BY-SA 3.0 |
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| Sep 25, 2013 at 10:17 | history | edited | Francesco Polizzi | CC BY-SA 3.0 |
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| Sep 25, 2013 at 9:52 | history | answered | Francesco Polizzi | CC BY-SA 3.0 |