Compactifications defined by arrangements, I: The ball quotient case

Compactifications defined by arrangements, I: The ball quotient case

Eduard Looijenga

Source: Duke Math. J. Volume 118, Number 1 (2003), 151-187.

Abstract

We define a natural compactification of an arrangement complement in a ball quotient. We show that when this complement has a moduli space interpretation, then this compactification is often one that appears naturally by means of geometric invariant theory. We illustrate this with the moduli spaces of smooth quartic curves and rational elliptic surfaces.

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First in series: Eduard Looijenga. Compactifications defined by arrangements, II: Locally symmetric varieties of type IV. Duke Math. J. Vol. 119, No. 3 (2003), pp. 527-588.

Project Euclid: euclid.dmj/1082744772

Primary Subjects: 14J15

Secondary Subjects: 32S22

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Permanent link to this document: http://projecteuclid.org/euclid.dmj/1082744557
Mathematical Reviews number (MathSciNet): MR1978885
Digital Object Identifier: doi:10.1215/S0012-7094-03-11816-5
Zentralblatt MATH identifier: 02032545

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