  We study the possibility of obtaining metastable de Sitter vacua of heterotic
string theory compactified on a Calabi-Yau threefold which are classical and
simple in the K\"ahler moduli sector of the theory. For this, we exploit a
known necessary condition on the K\"ahler potential in N=1-supergravity, which
we, under the assumption that only moduli fields contribute to supersymmetry
breaking, express in terms of a tensorial eigenvalue problem for the Calabi-Yau
triple intersection tensor. For three-dimensional moduli spaces we are able to
identify the discriminant of the Calabi-Yau intersection tensor in the
analysis, generalizing a known result for two-dimensional moduli spaces. We
also discuss explicit examples and possible generalizations.
