| In this thesis we use Witten's linear sigma models in conjunction with the mathematics of toric varieties to study the geometry of spacetime at short distances. An interesting result is that even in perturbative string theory, the topology of space is allowed to vary, though rather mildly, as a function of time. Nonperturbative corrections indicate that more drastic transitions can occur, in which the hodge numbers of the compactification manifold changes smoothly. This has a quantum mechanical interpretation in terms of black holes which are smoothly connected to elementary particles. |
