The Period Map for Cubic Threefolds

Abstract

Allcock-Carlson-Toledo dened 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 identication of the algebra of SL(5;C)-invariant polynomials on the representation space Sym3(C5) with an explicitly decribed algebra of meromorphic automorphic forms on the complex 10-ball.