Date of Award
Spring 1-1-2017
Document Type
Dissertation
Degree Name
Doctor of Philosophy (PhD)
First Advisor
Jonathan Wise
Second Advisor
Sebastian Casalaina-Martin
Third Advisor
Suion Ih
Fourth Advisor
Renzo Cavalieri
Fifth Advisor
Dhruv Ranganathan
Abstract
We clarify the definition of an infinitesimal automorphism of a log smooth curve, and show that logarithmic structure is capable of fixing the underlying infinitesimal automorphisms on a semistable curve. We then introduce the notion of an m-stable partially aligned logarithmic curve and construct a few natural semistable modular compactifications of the moduli space of smooth genus one curves. Finally, we prove that our moduli space of m-stable partially aligned log curves resolves the indeterminacy between the moduli space of Deligne-Mumford stable curves and the moduli space of m-stable curves constructed by Smyth.
Recommended Citation
Parker, Keli Siqueiros, "Semistable Modular Compactifications of Moduli Spaces of Genus One Curves" (2017). Mathematics Graduate Theses & Dissertations. 65.
https://scholar.colorado.edu/math_gradetds/65