Resumen de Lifting weighted blow-ups

Marco Andreatta

• Let f:X→Z be a local, projective, divisorial contraction between normal varieties of dimension n with Q -factorial singularities. Let Y⊂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 P∈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.