The period map for cubic threefolds
By E. Looijenga, R. Swierstra. Compositio Mathematica, 2006
47 citations recorded by the source corpus.
Allcock, Carlson and Toledo defined a period map for cubic threefolds which takes values in a ball quotient of dimension 10. A theorem of Voisin implies that this is an open embedding. We determine its image and show that on the algebraic level this amounts to identification of the algebra of $\operatorname{SL}(5,\mathbb{C})$-invariant polynomials on the representation space $\operatorname{Sym}^3(\mathbb{C}^5)^*$ with an explicitly described algebra of meromorphic automorphic forms on the complex 10-ball.
Subfields: Geometry and Topology, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/3d4c47d4dcc087c74be08e541748525c6a5df7ab
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In Geometry and Topology
In Mathematical Physics
Citations in the corpus
- Special cycles on unitary Shimura varieties II: global theory (2009, background): “ a few remarks. The compatibility with families is dueto the fact that the eigenspaces for the µ3-action and the Hodge filtration both vary in a holomorphic way. The point (ii) is [2], Thm. 1.1, resp. [54], Thm. 3.1, except that the stack aspect is neglected in these sources. However, the fact that w”
- The moduli space of cubic fourfolds via the period map (2007, background): “wer to a conjecture of Hassett [22, §4.4]. This builds on earlier results of Voisin [49] and Hassett [22], and was inspired by the recent work of Allcock–Carlson–Toledo [1, 2] and Looijenga–Swierstra [32] on the moduli space of cubic threefolds. Theorem 1.1. The image of the period map for cubic fou”
- Reflection groups in algebraic geometry (2006, background): “We give only one example, referring for more to [ 51 ], [50].”