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Author ORCID Identifier


Campus-Only Access for Five (5) Years

Document Type


Degree Name

Doctor of Philosophy (PhD)

Degree Program


Year Degree Awarded


Month Degree Awarded


First Advisor

Paul Hacking

Subject Categories

Algebraic Geometry


We study mirror symmetry for Miles Reid's 95 families of Q-Fano 3-folds Y. In accordance with mirror symmetry predictions, we show that the mirror of the log Calabi-Yau pair (Y,E) where E is an aticanonical divisor in |-KY| is a pair (X,D) together with a morphism W to the projective line whose general fiber F is a K3 surface and has exactly 3 singular fibers. We describe the general fiber of W explicitly, for instance, we give a formula for the Picard rank of F in terms of the singularities of Y. Finally, we use the theory of hypergeometric groups to describe the monodromy of the mirror family. In particular, we show that a power of the monodromy at infinitiy is maximally unipotent. This allows us to conclude that the fiber D over infinity after a base change and birational modifications yields a K3 surface of type III in Kulikov's notation.