Stable Limits of Log Surfaces and Cohen–Macaulay Singularities

Author: Hassett B.^{1, 2}

Source: Journal of Algebra, Volume 242, Number 1, August 2001 , pp. 225-235(11)

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Abstract:

Given a family of surfaces of general type over a smooth curve, one can apply semistable reduction and the minimal model program to obtain a stable reduction. This is the basis for a geometric compactification for moduli spaces of surfaces of general type, due to Kollár, Shepherd-Barron, and Alexeev. However, this approach hinges on the fact that the resulting stable limit has relatively mild singularities; in particular, it should be Cohen–Macaulay. Unfortunately, the standard formalism does not guarantee that stable limits of families of log surfaces are Cohen–Macaulay. Here we prove that this is the case. Copyright 2001 Academic Press.

Keywords: Cohen–; Macaulay; surfaces; moduli spaces

Language: English

Document Type: Research article

Affiliations: 1: Institute of Mathematical Sciences, Chinese University of Hong Kong, Room 501, Mong Man Wai Building, Shatin, Hong Kong 2: Department of Mathematics, MS 136, Rice University, 6100 South Main Street, Houston, Texas, 77005-1892

Publication date: 2001-08-01