The Period Map for Cubic Threefolds

Abstract

Allcock-Carlson-Toledo dened a period map for cubic threefoldswhich takes values in a ball quotient of dimension 10. A theoremof Voisin implies that this is an open embedding. We determine its imageand show that on the algebraic level this amounts to identication ofthe algebra of SL(5;C)-invariant polynomials on the representation spaceSym3(C5) with an explicitly decribed algebra of meromorphic automorphicforms on the complex 10-ball.