Timeline for What is known about the ample and effective cones of an Enriques surface?
Current License: CC BY-SA 2.5
6 events
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| Dec 13, 2010 at 19:16 | vote | accept | Vivek Shende | ||
| Oct 7, 2010 at 11:30 | comment | added | Dmitri Panov | Damiano, huge thanks!! This settles the question | |
| Oct 7, 2010 at 11:24 | history | edited | Dmitri Panov | CC BY-SA 2.5 |
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| Oct 7, 2010 at 7:38 | comment | added | damiano | On an Enriques surface, a nef divisor class $N$ is either effective or it is the canonical divisor $K$. Indeed, by Riemann-Roch, $\chi(N)=N^2/2+1>0$, and hence either $N$ or $K-N$ is effective. On the other hand, $N$ is nef and hence pseudo-effective, while $K$ is torsion and hence numerically trivial, so that $K-N$ is the opposite of a pseudo-effective class and it can be effective only if it is numerically trivial. Thus $K-N$ is effective only if it is zero, i.e. only if $N=K$. | |
| Oct 6, 2010 at 22:33 | history | edited | Dmitri Panov | CC BY-SA 2.5 |
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| Oct 6, 2010 at 22:19 | history | answered | Dmitri Panov | CC BY-SA 2.5 |