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10
votes
1
answer
887
views
Numerically equivalent effective divisors and semiampleness
Being semiample is not a numerical property (take for example torsion and a non-torsion divisor of degree 0 on a curve, or for more sophisticated examples just look at Lazarsfeld - Positivity in Algebraic …
8
votes
1
answer
942
views
volume of big line bundles under finite morphisms
(I know that if $B$ is not only big but also nef then the formula is true by Lazarsfeld's Positivity in Algebraic geometry I, remark 1.1.13, using the well-known fact that if $B$ is nef then vol($B$)=$ …