On the properness of the moduli space of stable surfaces

2006/01/13 by Michael A. van Opstall, van Opstall, Michael A. · 1 citation
Mathematics · #14J10 #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Geometric and Algebraic Topology #Homotopy and Cohomology in Algebraic Topology

paper · pdf · doi:10.48550/arxiv.math/0601345

openalex publication_date 2006/01/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The moduli spaces of stable surfaces serve as compactifications of the moduli spaces of canonical models of smooth surfaces in the same way the moduli spaces of stable curves compactify the moduli spaces of smooth curves. However, the natural definition of the moduli functor of stable surfaces allows in extra components parameterizing surfaces which do not smooth. This article verifies that these components are also proper.

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• Non-extendable MMPs

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