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Is there a name for a normal, projective variety such that every effective divisor is ample? Examples of such varieties are projective space, weighted projective spaces, and simple Abelian varieties Intersection of subvarieties versus ranks of Chow groups modulo numerical equivalences. If someone could also give a reference for the name, I would appreciate it. Thank you.

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    $\begingroup$ All your examples have Picard group of rank $1$. Conversely, every projective variety with Picard group of rank $1$ has this property. $\endgroup$
    – Sasha
    Commented Feb 21 at 4:52
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    $\begingroup$ In Francesco Polizi's answer in the referenced post he gave an example of such a variety where the Picard number is not one. $\endgroup$
    – Schemer1
    Commented Feb 21 at 7:43
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    $\begingroup$ Unless I miss something, the singleton satisfies this, but its Picard group has rank 0. $\endgroup$
    – YCor
    Commented Feb 21 at 10:41
  • $\begingroup$ For what it's worth, I am not familiar with any such name. $\endgroup$
    – Lazzaro Campeotti
    Commented Feb 22 at 10:37
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    $\begingroup$ Any K3 surface that does not contain a smooth rational or elliptic curve is also an example. These surfaces exist for every Picard rank up to 4. The reason these work can be generalized to give more examples. $\endgroup$
    – Sándor Kovács
    Commented Feb 23 at 4:14

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