2016/09/01 by Marco Andreatta, Andreatta, Marco
Mathematics · #14E30 (Primary) #14J40 #14N30 (Secondary) #Algebraic Geometry (math.AG) #FOS: Mathematics #math.AG #msc:14E30 #msc:14J40 #msc:14N30
paper · pdf · doi:10.48550/arxiv.1609.00156
11 pages, minor issues corrected. To appear in Revista Matematica Iberoamericana
arxiv created 2017/02/15 · arxiv updated 2017/02/16
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 -(KX + (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.