Lifting Weighted Blow-ups
Abstract
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-factorial singularity $P\in Z$, 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.
- Publication:
-
arXiv e-prints
- Pub Date:
- September 2016
- DOI:
- 10.48550/arXiv.1609.00156
- arXiv:
- arXiv:1609.00156
- Bibcode:
- 2016arXiv160900156A
- Keywords:
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- Mathematics - Algebraic Geometry;
- 14E30 (Primary);
- 14J40;
- 14N30 (Secondary)
- E-Print:
- 11 pages, minor issues corrected. To appear in Revista Matematica Iberoamericana