Minimal models and boundedness of stable varieties

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.

12 pages

References in corpus (4)

• Invariance of Plurigenera
• Log canonical singularities and complete moduli of stable pairs
• Weak semistable reduction in characteristic 0
• Deformations of canonical singularities

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• Compactifications of moduli of elliptic K3 surfaces: stable pair and toroidal
• Inversion of adjunction for rational and Du Bois pairs
• Higher-dimensional analogues of stable curves
• A study of the Hilbert-Mumford criterion for the stability of projective varieties
• On the hyperbolicity of base spaces for maximally variational families of smooth projective varieties
• Compactifications of smooth families and of moduli spaces of polarized manifolds
• G-marked moduli spaces
• Moduli of surfaces in ${\mathbb{P}}^3$
• Canonical models and stable reduction for plurifibered varieties
• On the Brody hyperbolicity of moduli spaces for canonically polarized manifolds
• Stable degenerations of symmetric squares of curves
• Moduli spaces of weighted pointed stable curves
• Moduli of products of curves