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For questions related to divisors in the sense of algebraic geometry (Cartier divisors, Weil divisors and so on). For question on divisors in the number theoretic sense please use the tag divisors-multiples.
1
vote
The kernel of a nef line bundle
I think this is a counterexample. Let $V = \mathbf P^2 \times \mathbf P^1$, $L= \mathscr{O}_{P^2} \boxtimes \mathscr{O}_{P^1}(1)$. Let $\ell_1, \ell_2$ be two distinct lines in $\mathbf{P}^2$ and let …
2
votes
Rational maps and Kodaira dimension
This is a point I've been confused about proving several times recently, so I'm going to write out the argument in (potentially excessive) detail.
As abx points out, $\phi^*$ gives an injection $H^0( …