| ABSTRACT |
From a singular projective variety X_0, one can potentially obtain a smooth variety by smoothing or via a crepant resolution. If X is a smoothing of X_0 and Y is a crepant resolution, we say that X and Y are related by extremal resolution. It is speculated that the moduli space of Calabi-Yau threefolds is connected via such transitions. Therefore, understanding the behavior of Gromov-Witten Theory under extremal transitions has important applications to mirror symmetry. In this talk I will describe a general procedure which produces extremal transitions between hypersurfaces in toric varieties and explain how their Gromov-Witten theories relate. Joint with Rongxiao Mi. |
