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Summary: EXPLICIT COMPACTIFICATIONS OF MODULI SPACES
OF CAMPEDELLI AND BURNIAT SURFACES
VALERY ALEXEEV AND RITA PARDINI
Abstract. We describe the compactifications obtained by adding slc surfaces X with ample KX, for two
connected components in the moduli space of surfaces of general type: Campedelli surfaces with 1(X) = Z3
2,
and Burniat surfaces with K2
X = 6.
This is the color version; black-and-white version at http://www.math.uga.edu/~valery/ap-bw.pdf
Contents
Introduction 1
1. Campedelli and Burniat surfaces 2
2. Compactifying the moduli of line arrangements 4
2.1. Campedelli arrangements 4
2.2. Degenerations of Burniat arrangements 4
2.3. Compactified moduli of Burniat arrangements 9
3. Non-normal Zk
2 covers f : X Y 12
3.1. The case of normal Y 12
3.2. The general case 14
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