Minimal models and boundedness of stable varieties

1998/04/08 by Kalle Karu, Karu, Kalle
Mathematics · #14D22 #14J10 #Algebraic Geometry (math.AG) #FOS: Mathematics #math.AG #msc:14D22 #msc:14J10

paper · pdf · doi:10.48550/arxiv.math/9804049

12 pages

arxiv created 1998/04/08 · arxiv updated 2009/11/30

Abstract

We consider a class of stable smoothable n-dimensional varieties, the analogs of stable curves. Assuming the minimal model program in dimension n+1, we prove that this class is bounded. From Kollar's method of constructing projective moduli spaces we get as a corollary that minimal model program in dimension n+1 implies the existence of a projective coarse moduli space for stable smoothable n-folds.

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