Lifting weighted blow-ups

@article{Andreatta2018LiftingWB,
  title={Lifting weighted blow-ups},
  author={Marco Andreatta},
  journal={Revista Matem{\'a}tica Iberoamericana},
  year={2018}
}
  • M. Andreatta
  • Published 1 September 2016
  • Mathematics
  • Revista Matemática Iberoamericana
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… 
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