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edit approved Apr 7, 2021 at 15:34
user875280
edit approved Apr 7, 2021 at 15:34
user875280
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Let $D$ be a divisor on a (complex) K3 surface.

Suppose $D^2\geq0$. In general, $D$ is nef if $D\cdot C\geq0$ for all irreducible curves on the surface.

Is it sufficient in our case sufficient to to check this for smooth rational curves (i.e. the (-2) curves) ?

Let $D$ be a divisor on a (complex) K3 surface.

Suppose $D^2\geq0$. In general, $D$ is nef if $D\cdot C\geq0$ for all irreducible curves on the surface.

Is in our case sufficient to check this for smooth rational curves (i.e. the (-2) curves) ?

Let $D$ be a divisor on a (complex) K3 surface.

Suppose $D^2\geq0$. In general, $D$ is nef if $D\cdot C\geq0$ for all irreducible curves on the surface.

Is it sufficient in our case to check this for smooth rational curves (i.e. the (-2) curves) ?

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Heitor
Heitor
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Nefness on a K3 surface

Let $D$ be a divisor on a (complex) K3 surface.

Suppose $D^2\geq0$. In general, $D$ is nef if $D\cdot C\geq0$ for all irreducible curves on the surface.

Is in our case sufficient to check this for smooth rational curves (i.e. the (-2) curves) ?