Journal of Differential Geometry

Asphericity of Moduli Spaces via Curvature

Daniel Allcock

Abstract

We show that under suitable conditions a branched cover satisfies the same upper curvature bounds as its base space. First we do this when the base space is a metric space satisfying Alexandrov's curvature condition CAT(κ) and the branch locus is complete and convex. Then we treat branched covers of a Riemannian manifold over suitable mutually orthogonal submanifolds. In neither setting do we require that the branching be locally finite. We apply our results to hyperplane complements in several Hermitian symmetric spaces of nonpositive sectional curvature in order to prove that two moduli spaces arising in algebraic geometry are aspherical. These are the moduli spaces of the smooth cubic surfaces in ℂP3 and of the smooth complex Enriques surfaces.

Article information

Source
J. Differential Geom., Volume 55, Number 3 (2000), 441-451.

Dates
First available in Project Euclid: 20 July 2004

Permanent link to this document
https://projecteuclid.org/euclid.jdg/1090341260

Digital Object Identifier
doi:10.4310/jdg/1090341260

Mathematical Reviews number (MathSciNet)
MR1863730

Zentralblatt MATH identifier
1067.53028

Citation

Allcock, Daniel. Asphericity of Moduli Spaces via Curvature. J. Differential Geom. 55 (2000), no. 3, 441--451. doi:10.4310/jdg/1090341260. https://projecteuclid.org/euclid.jdg/1090341260


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