CONIFOLD TRANSITIONS AND ASPECTS OF DUALITY

Recent work by Greene, Morrison and Strominger has lead to a consisten t physical interpretation of certain types of transitions between diff erent string vacua. These transitions, discovered several years ago, i nvolve singular conifold configurations which connect distinct Calabi- Yau manifolds. In this paper we generalize the splitting conifold tran sition to weighted manifolds and describe a class of connections betwe en the webs of ordinary and weighted projective Calabi-Yau spaces. Com bining these two constructions we find evidence for a dual analog of c onifold transitions in heterotic N = 2 compactifications on K3 x T-2 a nd describe the first conifold transition of a Calabi-Yau manifold who se heterotic dual has been identified by Kachru and Vafa. We furthermo re present a special type of conifold transition which, when applied t o certain classes of Calabi-Yau K3 fibrations, preserves the fiber str ucture. Along the way we describe a new phenomenon which occurs when h ypersurface singularities 'collide' with orbifold singularities. Final ly we point out the importance of weighted conifold transitions which are not of splitting type. Such non-splitting conifold transitions tur n out to connect the known web of Calabi-Yau spaces to new regions of the collective moduli space.