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Anticanonical Models Of Smoothings Of Cyclic Quotient Singularities, Arie A. Stern Gonzalez
Anticanonical Models Of Smoothings Of Cyclic Quotient Singularities, Arie A. Stern Gonzalez
Doctoral Dissertations
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 …