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The Period Map for Cubic Threefolds

By E. Looijenga and R. Swierstra


Allcock-Carlson-Toledo de#2;ned a period map for cubic threefolds\ud which takes values in a ball quotient of dimension 10. A theorem\ud of Voisin implies that this is an open embedding. We determine its image\ud and show that on the algebraic level this amounts to identi#2;cation of\ud the algebra of SL(5;C)-invariant polynomials on the representation space\ud Sym3(C5)#3; with an explicitly decribed algebra of meromorphic automorphic\ud forms on the complex 10-ball

Topics: Wiskunde en Informatica
Year: 2006
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