Lifting Weighted Blowups
Abstract
Let f: X > Z be a local, projective, divisorial contraction between normal varieties of dimension n with Qfactorial singularities. Let $Y \subset X$ be a fample Cartier divisor and assume that fY: Y > W has a structure of a weighted blowup. We prove that f: X > Z, as well, has a structure of weighted blowup. As an application we consider a local projective contraction f: X > Z from a variety X with terminal Qfactorial singularities, which contracts a prime divisor E to an isolated Qfactorial singularity $P\in Z$, such that $(K_X + (n3)L)$ is fample, for a fample Cartier divisor L on X. We prove that (Z,P) is a hyperquotient singularity and f is a weighted blowup.
 Publication:

arXiv eprints
 Pub Date:
 September 2016
 arXiv:
 arXiv:1609.00156
 Bibcode:
 2016arXiv160900156A
 Keywords:

 Mathematics  Algebraic Geometry;
 14E30 (Primary);
 14J40;
 14N30 (Secondary)
 EPrint:
 11 pages, minor issues corrected. To appear in Revista Matematica Iberoamericana