The Moduli Space of Cubic Threefolds As a Ball Quotient

By Daniel Allcock, J. Carlson, D. Toledo. 2006

104 citations recorded by the source corpus.

The moduli space of cubic threefolds in $\mathbb{C}P^4$, with some minor birational modifications, is the Baily-Borel compactification of the quotient of the complex 10-ball by a discrete group. The authors describe both the birational modifications and the discrete group explicitly.|The moduli space of cubic threefolds in $\mathbb{C}P^4$, with some minor birational modifications, is the Baily-Borel compactification of the quotient of the complex 10-ball by a discrete group. The authors describe both the birational modifications and the discrete group explicitly.

Subfields: Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/66ec96562401437ae1a67de1339f6da81940af1b

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In Geometry and Topology

In Mathematical Physics

Citations in the corpus

The moduli space of cubic fourfolds (2007, result): “) boundary from Shah [33]. We close by noting that there is also a close relation to the results of Allcock [1] for cubic threefolds. Therelation is given by Allcock-Carlson-Toledo (ACT) construction [2], which associates to a cubic threefold f(x 0,...,x 4) the cubic fourfold f(x 0,...,x 4)+x35. Spe”
Reflection groups in algebraic geometry (2006, result): “GEBRAIC GEOMETRY 15 Table 2. Finite complex reﬂection groups Number Name Order dimE Degrees 1 An = Σn+1 (n+1)! n 2,3,...,n+1 2 G(m,p,n) mnn!/p n m,m +1,...,(n−1)m,mn/p 3 []m m 1 m 4 3[3]3 24 2 4,6 5 3[4]3 72 2 6,12 6 3[6]2 48 2 4,12 7 < 3,3,3 > 2 144 2 12,12 8 4[3]4 96 2 8,12 9 4[6]2 192 2 8,2”
The moduli space of cubic fourfolds via the period map (2007, background): “the statement that the spectrum of those singularities (in dimension 4) is included in the interval [1, 2] (see also remark 3.”
The period map for cubic threefolds (2006, background): “This journal is c© Foundation Compositio Mathematica 2007. construction applied to a cubic surface yields a cubic threefold with µ3-action (and, hence, gives rise to a cubic fourfold with µ3 ×µ3-action).”
Braid groups and Hodge theory (2013, unknown): “[DK], [Ko], [ACT1], [ACT2], [Al2], [Lo2].”