Finiteness of monodromy for fibered Calabi-Yau threefolds

François Greer, Michigan State University

An old question going back to S.T. Yau asks whether there are finitely many diffeomorphism types for smooth projective Calabi-Yau manifolds of a given dimension. The answer is affirmative for dimensions one and two (elliptic curves and K3 surfaces). It has recently been settled for Calabi-Yau threefolds admitting elliptic fibrations. We discuss the case of CY3’s admitting abelian surface or K3 fibrations. 

MC 5417