The Complex Hyperbolic Geometry of the Moduli Space of Cubic Surfaces

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dc.creatorAllcock, Daniel
dc.creatorCarlson, James A.
dc.creatorToledo, Domingo
dc.date2000-07-09
dc.date.accessioned2026-07-07T04:36:18Z
dc.date.available2026-07-07T04:36:18Z
dc.descriptionRecall that the moduli space of smooth (that is, stable) cubic curves is isomorphic to the quotient of the upper half plane by the group of fractional linear transformations with integer coefficients. We establish a similar result for stable cubic surfaces: the moduli space is biholomorphic to a quotient of the compex 4-ball by an explict arithmetic group generated by complex reflections. This identification gives interesting structural information on the moduli space and allows one to locate the points in complex hyperbolic 4-space corresponding to cubic surfaces with symmetry, e.g., the Fermat cubic surface. Related results, not quite as extensive, were announced in alg-geom/9709016.
dc.descriptionAlso available at http://www.math.utah.edu/~carlson/research/eprints
dc.identifierhttps://arxiv.org/abs/math/0007048
dc.identifierhttp://arxiv.org/abs/math/0007048
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/59546
dc.subjectAlgebraic Geometry
dc.subject14C30, 14J10, 22E40
dc.titleThe Complex Hyperbolic Geometry of the Moduli Space of Cubic Surfaces
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