# On the properness of the moduli space of stable surfaces

Research paper by Michael A. van Opstall

Indexed on: 17 Apr '06Published on: 17 Apr '06Published in: Mathematics - Algebraic Geometry

#### 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.