Let f: X -> Z be a local, projective, divisorial contraction between normal varieties of dimension n with Q-factorial singularities. Let $Y subset X$ be a f-ample Cartier divisor and assume that f|Y: Y -> W has a structure of a weighted blow-up. We prove that f: X -> Z, as well, has a structure of weighted blow-up. As an application we consider a local projective contraction f: X -> Z from a variety X with terminal Q-factorial singularities, which contracts a prime divisor E to an isolated Q-factorial singularity $Pin Z$, such that $-(K_X + (n-3)L)$ is f-ample, for a f-ample Cartier divisor L on X. We prove that (Z,P) is a hyperquotient singularity and f is a weighted blow-up.

Lifting Weighted Blow-ups / Andreatta, Marco. - In: REVISTA MATEMATICA IBEROAMERICANA. - ISSN 0213-2230. - 34:4(2018), pp. 1809-1820. [10.4171/rmi/1044]

Lifting Weighted Blow-ups

Marco Andreatta
2018-01-01

Abstract

Let f: X -> Z be a local, projective, divisorial contraction between normal varieties of dimension n with Q-factorial singularities. Let $Y subset X$ be a f-ample Cartier divisor and assume that f|Y: Y -> W has a structure of a weighted blow-up. We prove that f: X -> Z, as well, has a structure of weighted blow-up. As an application we consider a local projective contraction f: X -> Z from a variety X with terminal Q-factorial singularities, which contracts a prime divisor E to an isolated Q-factorial singularity $Pin Z$, such that $-(K_X + (n-3)L)$ is f-ample, for a f-ample Cartier divisor L on X. We prove that (Z,P) is a hyperquotient singularity and f is a weighted blow-up.
2018
4
Andreatta, Marco
Lifting Weighted Blow-ups / Andreatta, Marco. - In: REVISTA MATEMATICA IBEROAMERICANA. - ISSN 0213-2230. - 34:4(2018), pp. 1809-1820. [10.4171/rmi/1044]
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11572/194101
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