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Author ORCID Identifier
https://orcid.org/0000-0002-2025-4126
AccessType
Campus-Only Access for Five (5) Years
Document Type
dissertation
Degree Name
Doctor of Philosophy (PhD)
Degree Program
Mathematics
Year Degree Awarded
2024
Month Degree Awarded
February
First Advisor
Paul Hacking
Subject Categories
Algebraic Geometry
Abstract
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.
DOI
https://doi.org/10.7275/36515900
Recommended Citation
Rodriguez Avila, Cristian A., "MIRROR SYMMETRY FOR Q-FANO 3-FOLDS" (2024). Doctoral Dissertations. 3087.
https://doi.org/10.7275/36515900
https://scholarworks.umass.edu/dissertations_2/3087