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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

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