Landau-Ginzburg vacua of string, M- and F-theory at c=12

Theories in more than ten dimensions play an important role in understanding non-perturbative aspects of string theory. Consistent compactifications of such theories can be constructed via Calabi-Yau fourfolds. These models can be analyzed particularly efficiently in the Landau-Ginzburg phase of the linear a-model, when available. In the present paper we focus on those a-models which have both a Landau-Ginzburg phase and a geometric phase described by hypersurfaces in weighted projective five-space. We describe some of the pertinent properties of these models, such as the cohomology, the connectivity of the resulting moduli space, and mirror symmetry among the 1,100,055 configurations which we have constructed. (C) 1999 Published by Elsevier Science B.V. All rights reserved.