Date of Award
2024
Document Type
Dissertation
Degree Name
Doctor of Philosophy (PhD)
Department
Mathematics
First Advisor
Taylor Dupuy
Second Advisor
Christelle Vincent
Abstract
We compute the canonical ring of some stacks. We first give a detailed account of what this problem means including several proofs of a famous historical example. The main body of work of this thesis expands on our article \cite{Franklin-geometry-Drinfeld-modular-forms} in describing the geometry of Drinfeld modular forms as sections of a specified line bundle on a certain stacky modular curve. As a consequence of that geometry, we provide a program: one can compute the (log) canonical ring of a stacky curve to determine generators and relations for an algebra of Drinfeld modular forms, answering a problem posed by Gekeler in $1986.$
Language
en
Number of Pages
217 p.
Recommended Citation
Franklin, Jesse, "Computing the Canonical Ring of Certain Stacks" (2024). Graduate College Dissertations and Theses. 1838.
https://scholarworks.uvm.edu/graddis/1838