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Timeline for Nefness on a K3 surface

Current License: CC BY-SA 3.0

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Nov 12, 2013 at 17:54 comment added Abhinav Kumar Not if the divisor $D$ is reducible - else take $D = C + f$ on a Hirzebruch surface with $C^2 = -2, f^2 = 0, C \cdot f = 1$, and notice $D \cdot C = -1$. If you don't assume $D$ is effective, then Jason's comment shows you that there's no way to distinguish $D$ from its negative.
Nov 12, 2013 at 17:15 comment added Heitor Wait a moment. But if $D$ is effective and $D^2\geq 0$ then $D$ is nef on any surface, isn't it?
Nov 12, 2013 at 17:08 vote accept Heitor
Nov 12, 2013 at 17:12
Nov 12, 2013 at 14:12 history answered Abhinav Kumar CC BY-SA 3.0