Lifting weighted blow-ups

• Marco Andreatta ^[1]
  1. [1] Università di Trento, Povo
• Localización: Revista matemática iberoamericana, ISSN 0213-2230, Vol. 34, Nº 4, 2018, págs. 1809-1820
• Idioma: inglés
• DOI: 10.4171/rmi/1044
• Texto completo no disponible (Saber más ...)
• Resumen

  • 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.