isAmple D
A Cartier divisor is very ample when it is basepoint free and the map arising from its complete linear series is a closed embedding. A Cartier divisor is ample when some positive integer multiple is very ample. For a torus-invariant Cartier divisor on a complete normal toric variety, the following conditions are equivalent:
On projective space, every torus-invariant irreducible divisor is ample.
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On a Hirzebruch surface, none of the torus-invariant irreducible divisors are ample.
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A normal toric variety is Fano if and only if its anticanonical divisors, namely minus the sum of its torus-invariant irreducible divisors, is ample.
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