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A complex ball uniformization of the moduli space of cubic surfaces via periods of K 3 surfaces

Identifieur interne : 000D10 ( Main/Exploration ); précédent : 000D09; suivant : 000D11

A complex ball uniformization of the moduli space of cubic surfaces via periods of K 3 surfaces

Auteurs : I. Dolgachev ; B. Van Geemen ; S. Kond

Source :

RBID : ISTEX:A513D11A699D4AB771C80A05700DC1F776E3009F

English descriptors

Abstract

In this paper we show that the moduli space of nodal cubic surfaces is isomorphic to a quotient of a 4-dimensional complex ball by an arithmetic subgroup of the unitary group. This complex ball uniformization uses the periods of certain K 3 surfaces which are naturally associated to cubic surfaces. A similar uniformization is given for different covers of the moduli space corresponding to geometric markings of the Picard group or a choice of a line on the surface. We also give a detailed description of the boundary components corresponding to singular surfaces.

Url:
DOI: 10.1515/crll.2005.2005.588.99


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Le document en format XML

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<term>Equivariant isomorphism</term>
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<term>Geometric markings</term>
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<term>Linear system</term>
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<term>Minimal resolution</term>
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<term>Mncub mncub</term>
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<term>Orthogonal complement</term>
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<term>Permutation</term>
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<term>Pezzo surface</term>
<term>Pezzo surfaces</term>
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<term>Picard lattice</term>
<term>Point sets</term>
<term>Quadratic form</term>
<term>Quadric bundle</term>
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<term>Reducible</term>
<term>Resp</term>
<term>Root lattice</term>
<term>Segre</term>
<term>Singular point</term>
<term>Singular points</term>
<term>Stabilizer</term>
<term>Stable pair</term>
<term>Standard elliptic</term>
<term>Subgroup</term>
<term>Sublattice</term>
<term>Subset</term>
<term>Transcendental cycles</term>
<term>Transitively</term>
<term>Trivially</term>
<term>Type vector</term>
<term>Uniformization</term>
<term>Unimodular lattice</term>
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<front>
<div type="abstract" xml:lang="en">In this paper we show that the moduli space of nodal cubic surfaces is isomorphic to a quotient of a 4-dimensional complex ball by an arithmetic subgroup of the unitary group. This complex ball uniformization uses the periods of certain K 3 surfaces which are naturally associated to cubic surfaces. A similar uniformization is given for different covers of the moduli space corresponding to geometric markings of the Picard group or a choice of a line on the surface. We also give a detailed description of the boundary components corresponding to singular surfaces.</div>
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