Lifting weighted blow-ups
Marco Andreatta
Università di Trento, Povo (Trento), Italy
![Lifting weighted blow-ups cover](/_next/image?url=https%3A%2F%2Fcontent.ems.press%2Fassets%2Fpublic%2Fimages%2Fserial-issues%2Fcover-rmi-volume-34-issue-4.png&w=3840&q=90)
Abstract
Let be a local, projective, divisorial contraction between normal varieties of dimension with -factorial singularities.
Let be a -ample Cartier divisor and assume that has a structure of a weighted blow-up. We prove that , as well, has a structure of weighted blow-up.
As an application we consider a local projective contraction from a variety with terminal -factorial singularities, which contracts a prime divisor to an isolated -factorial singularity , such that is -ample, for a -ample Cartier divisor on . We prove that is a hyperquotient singularity and is a weighted blow-up.
Cite this article
Marco Andreatta, Lifting weighted blow-ups. Rev. Mat. Iberoam. 34 (2018), no. 4, pp. 1809–1820
DOI 10.4171/RMI/1044