Date of Award

Spring 1-1-2017

Document Type

Dissertation

Degree Name

Doctor of Philosophy (PhD)

First Advisor

Jonathan Wise

Second Advisor

Dhruv Ranganathan

Third Advisor

Sebastian Casalaina-Martin

Fourth Advisor

Suion Ih

Fifth Advisor

Renzo Cavalieri

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.

Included in

Mathematics Commons

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