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Inspired by the ideas of the minimal model program, Shepherd-Barron, Kollár, and Alexeev have constructed a geometric compactification for the moduli space of surfaces of log general type. In this paper, we discuss one of the simplest examples that fits into this framework: the case of pairs consisting of a degree two surface and an ample divisor . Specifically, we construct and describe explicitly a geometric compactification for the moduli of degree two pairs. This compactification...
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