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Author ORCID Identifier
https://orcid.org/0000-0002-1361-0153
AccessType
Open Access Dissertation
Document Type
dissertation
Degree Name
Doctor of Philosophy (PhD)
Degree Program
Mathematics
Year Degree Awarded
2022
Month Degree Awarded
February
First Advisor
Jenia Tevelev
Second Advisor
Paul Hacking
Third Advisor
Eyal Markman
Fourth Advisor
David Barrington
Subject Categories
Algebraic Geometry
Abstract
In this thesis we study anticanonical models of smoothings of cyclic quotient singularities. Given a surface cyclic quotient singularity $Q\in Y$, it is an open problem to determine all smoothings of $Y$ that admit an anticanonical model and to compute it. In \cite{HTU}, Hacking, Tevelev and Urz\'ua studied certain irreducible components of the versal deformation space of $Y$, and within these components, they found one parameter smoothings $\Y \to \A^1$ that admit an anticanonical model and proved that they have canonical singularities. Moreover, they compute explicitly the anticanonical models that have terminal singularities using Mori's division algorithm \cite{M02}. We study one parameter smoothings in these components that admit an anticanonical model with canonical but non-terminal singularities with the goal of classifying them completely. We identify certain class of ``diagonal" smoothings where the total space is a toric threefold and we construct the anticanonical model explicitly using the toric MMP.
DOI
https://doi.org/10.7275/27487488.0
Recommended Citation
Stern Gonzalez, Arie A., "ANTICANONICAL MODELS OF SMOOTHINGS OF CYCLIC QUOTIENT SINGULARITIES" (2022). Doctoral Dissertations. 2477.
https://doi.org/10.7275/27487488.0
https://scholarworks.umass.edu/dissertations_2/2477