Why $-(K_X+D)$ is $f$-ample if $phi:(X, D)to Y$ is a small contraction?

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We assume that $f:Xto S$ is a projective morphism, and $phi:(X, D)to Y$ is a small contraction, i.e $phi$ is a birational contraction with codim Ex$(f)geq2$.
Then, is $-(K_X+D)$ $f$-ample ?



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    This question has some issues: confusion between $f$ and $phi$, the role of $S$, etc. But nevertheless the answer is no. If this question is coming from something you read, I suggest that you check the source carefully and come back and update your question if needed.
    – Asal Beag Dubh
    Aug 18 at 8:25














up vote
0
down vote

favorite












We assume that $f:Xto S$ is a projective morphism, and $phi:(X, D)to Y$ is a small contraction, i.e $phi$ is a birational contraction with codim Ex$(f)geq2$.
Then, is $-(K_X+D)$ $f$-ample ?



Please let me know.







share|cite|improve this question


















  • 3




    This question has some issues: confusion between $f$ and $phi$, the role of $S$, etc. But nevertheless the answer is no. If this question is coming from something you read, I suggest that you check the source carefully and come back and update your question if needed.
    – Asal Beag Dubh
    Aug 18 at 8:25












up vote
0
down vote

favorite









up vote
0
down vote

favorite











We assume that $f:Xto S$ is a projective morphism, and $phi:(X, D)to Y$ is a small contraction, i.e $phi$ is a birational contraction with codim Ex$(f)geq2$.
Then, is $-(K_X+D)$ $f$-ample ?



Please let me know.







share|cite|improve this question














We assume that $f:Xto S$ is a projective morphism, and $phi:(X, D)to Y$ is a small contraction, i.e $phi$ is a birational contraction with codim Ex$(f)geq2$.
Then, is $-(K_X+D)$ $f$-ample ?



Please let me know.









share|cite|improve this question













share|cite|improve this question




share|cite|improve this question








edited Aug 25 at 1:08









Stefano

2,123730




2,123730










asked Aug 18 at 1:59









ag_taro

41




41







  • 3




    This question has some issues: confusion between $f$ and $phi$, the role of $S$, etc. But nevertheless the answer is no. If this question is coming from something you read, I suggest that you check the source carefully and come back and update your question if needed.
    – Asal Beag Dubh
    Aug 18 at 8:25












  • 3




    This question has some issues: confusion between $f$ and $phi$, the role of $S$, etc. But nevertheless the answer is no. If this question is coming from something you read, I suggest that you check the source carefully and come back and update your question if needed.
    – Asal Beag Dubh
    Aug 18 at 8:25







3




3




This question has some issues: confusion between $f$ and $phi$, the role of $S$, etc. But nevertheless the answer is no. If this question is coming from something you read, I suggest that you check the source carefully and come back and update your question if needed.
– Asal Beag Dubh
Aug 18 at 8:25




This question has some issues: confusion between $f$ and $phi$, the role of $S$, etc. But nevertheless the answer is no. If this question is coming from something you read, I suggest that you check the source carefully and come back and update your question if needed.
– Asal Beag Dubh
Aug 18 at 8:25















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