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Results tagged with divisors
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user 104695
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
Extending effective Cartier divisors
Take two planes $D_1 = V(x),D_2=V(y)\subset \mathbb{P}^3_{(x:y:z:t)}$ and consider the line $C=V(x,z)\subset D_1$. The equation of any hypersurface $D=V(f)$ of degree $d$ which only meets $D_2$ in the …
- 1,306
3
votes
Is this divisorial contraction a blow-up?
This $f$ is the blowup of $C$. See qu. 22 of Kollár's Exercises in the birational geometry of algebraic varieties.
A subtle point is whether you assume that $C$ is irreducible or not.
If $C$ is irr …
- 1,306
9
votes
Accepted
A question on "Ample subvarieties of algebraic varieties"
I suspect that you are supposed to view the projective variety $X$ as being given with a chosen projective embedding $X\subset \mathbb P^n$, and therefore a distinguished ample divisor $\mathcal{O}_X( …
- 1,306
5
votes
Accepted
Existence of terminal $3$-fold flips
Yes - there are very many such examples, and you can cook up examples by a procedure called 'Mori's algorithm'.
A k2A flipping neighbourhood is a 3-fold flipping contraction $f\colon(C\subset X)\to (P …
- 1,306
3
votes
Accepted
Definition of canonical pair
You are using the wrong equation to compute discrepancies. It should be
$$ K_Y = f^*(K_X + D) + \sum a_E(X,D) E $$
where the $E$ are not all necessarily exceptional.
For example if $(X,D)$ is already …
- 1,306