# 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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## References

SHOWING 1-10 OF 25 REFERENCES
FANO-MORI CONTRACTIONS OF HIGH LENGTH ON PROJECTIVE VARIETIES WITH TERMINAL SINGULARITIES
• Mathematics
• 2014
Let X be a projective variety with Q-factorial terminal singulari- ties and let L be an ample Cartier divisor on X. We prove that if f is a birational contraction associated to an extremal ray RNE(X)
Three-fold divisorial contractions to singularities of higher indices
We complete the explicit study of a three-fold divisorial contraction whose exceptional divisor contracts to a point, by treating the case where the point downstairs is a singularity of index $n \ge Divisorial contractions to 3-dimensional terminal singularities with discrepancy one We study a divisorial contraction … : Y ! X such that … contracts an irreducible divisor E to a point P and that the discrepancy of E is 1 when P 2 X is a 3-dimensional terminal singularity of type Local Fano-Mori contractions of high nef-value • Mathematics • 2014 Let$X$be a variety with at most terminal$\mathbb Q$-factorial singularities of dimension$n$. We study local contractions$f:X\to Z$supported by a$\mathbb Q$-Cartier divisor of the type$K_X+
Supplement to classification of three-fold divisorial contractions
Every three-fold divisorial contraction to a non-Gorenst ein point is a weighted blow-up. This supplement finishes the explicit description of a three -fold divisorial contraction whose exceptional
MINIMAL MODEL PROGRAM WITH SCALING AND ADJUNCTION THEORY
Let (X, L) be a quasi-polarized pair, i.e. X is a normal complex projective variety and L is a nef and big line bundle on it. We study, up to birational equivalence, the positivity (nefness) of the
General elephants of three-fold divisorial contractions
The theory of minimal models has enriched the study of higher-dimensional algebraic geometry; see [10] and [12]. For a variety with mild singularities, this theory produces another variety which
Toward a numerical theory of ampleness
Introduction Chapter I. Intersection Numbers ? 1. The polynomial theorem of Snapper ? 2. The definition and some properties of intersection numbers ? 3. Degrees and Hilbert polynomials ? 4.
Divisorial contractions in dimension three which contract divisors to smooth points
Abstract.We deal with a divisorial contraction in dimension three which contracts its exceptional divisor to a smooth point. We prove that any such contraction can be obtained by a suitable weighted
Divisorial Contractions in Dimension Three which Contract Divisors to Compound A1 Points
We deal with a divisorial contraction in dimension three which contracts its exceptional divisor to a compound A1 point. We prove that any such contraction is obtained by a suitable weighted blow-up.