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Author ORCID Identifier
https://orcid.org/0000-0003-4123-886X
AccessType
Open Access Dissertation
Document Type
dissertation
Degree Name
Doctor of Philosophy (PhD)
Degree Program
Mathematics
Year Degree Awarded
2021
Month Degree Awarded
May
First Advisor
Paul Hacking
Subject Categories
Algebraic Geometry
Abstract
In 1993, Morrison conjectured that the automorphism group of a Calabi-Yau 3-fold acts on its nef cone with a rational polyhedral fundamental domain. In this thesis, we prove a version of this conjecture for log Calabi-Yau surfaces. In particular, for a generic log Calabi-Yau surface with singular boundary, the monodromy group acts on the nef effective cone with a rational polyhedral fundamental domain. In addition, the automorphism group of the unique surface with a split mixed Hodge structure in each deformation type acts on the nef effective cone with a rational polyhedral fundamental domain. We also prove that, given a log Calabi-Yau surface with a split mixed Hodge structure, if the boundary length is no greater than six, then the cone of curves is finitely generated. Moreover, we explicitly describe these cones. This provides infinite series of new examples of Mori Dream spaces.
DOI
https://doi.org/10.7275/22237971.0
Recommended Citation
Li, Jennifer, "A Cone Conjecture for Log Calabi-Yau Surfaces" (2021). Doctoral Dissertations. 2194.
https://doi.org/10.7275/22237971.0
https://scholarworks.umass.edu/dissertations_2/2194