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We study the possibility of obtaining metastable de Sitter vacua of heteroticstring theory compactified on a Calabi-Yau threefold which are classical andsimple in the K\"ahler moduli sector of the theory. For this, we exploit aknown necessary condition on the K\"ahler potential in N=1-supergravity, whichwe, under the assumption that only moduli fields contribute to supersymmetrybreaking, express in terms of a tensorial eigenvalue problem for the Calabi-Yautriple intersection tensor. For three-dimensional moduli spaces we are able toidentify the discriminant of the Calabi-Yau intersection tensor in theanalysis, generalizing a known result for two-dimensional moduli spaces. Wealso discuss explicit examples and possible generalizations.

Constraints from de Sitter metastability in heterotic string compactifications