Timeline for Disjoint curves in an algebraic surface
Current License: CC BY-SA 3.0
5 events
| when toggle format | what | by | license | comment | |
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| Mar 23, 2015 at 15:10 | history | edited | Roberto Pignatelli | CC BY-SA 3.0 |
fixed grammar
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| Mar 23, 2015 at 14:50 | comment | added | Roberto Pignatelli | The assumption $p_g=0$ gives $h^2(X,{\mathbb C})=h^{1,1}$ and therefore $H^2(X,{\mathbb Q}) \subset H^{1,1}$: these surfaces have automatically maximal Picard number. | |
| Mar 23, 2015 at 14:19 | comment | added | abx | These surfaces are projective, hence $H^2(S,\Bbb{Q})$ is spanned by the class of an ample divisor. And, yes, a curve of negative square on a smooth surface can always be contracted. | |
| Mar 23, 2015 at 13:04 | comment | added | Marco Golla | Is it automatic that for all these surfaces there is a holomorphic curve representing some nontrivial homology class? Also, why can you always contract negative curves? (This could well be a standard argument I am not aware of...) | |
| Mar 23, 2015 at 9:25 | history | answered | Roberto Pignatelli | CC BY-SA 3.0 |