The period map for cubic fourfolds |
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Authors: | Eduard Looijenga |
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Institution: | (1) Mathematisch Instituut, Universiteit Utrecht, P.O. Box 80.010, 3508 TA Utrecht, Netherlands |
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Abstract: | The period map for cubic fourfolds takes values in a locally symmetric variety of orthogonal type of dimension 20. We determine
the image of this period map (thus confirming a conjecture of Hassett) and give at the same time a new proof of the theorem
of Voisin that asserts that this period map is an open embedding. An algebraic version of our main result is an identification
of the algebra of SL (6,ℂ)-invariant polynomials on the representation space Sym 3(ℂ6)* with a certain algebra of meromorphic automorphic forms on a symmetric domain of orthogonal type of dimension 20. We also
describe the stratification of the moduli space of semistable cubic fourfolds in terms of a Vinberg-Dynkin diagram. |
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Keywords: | Mathematics Subject Classification (2000)" target="_blank">Mathematics Subject Classification (2000) 32G20 14J35 32N15 |
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