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Weakly Proper Moduli Stacks of Curves by Alper, Jarod; Smyth, David Ishii; van der Wyck, Frederick is a scholarly article available to read on EtoBox.

What is Weakly Proper Moduli Stacks of Curves about?

This is the first in a projected series of three papers in which we construct the second flip in the log minimal model program for $\bar{M}_g$. We introduce the notion of a weakly proper algebraic stack, which may be considered as an abstract characterization of those mildly non-separated moduli problems encountered in the context of Geometric Invariant Theory (GIT), and develop techniques for proving that a stack is weakly proper without the usual semistability analysis of GIT. We define a sequence of moduli stacks of curves involving nodes, cusps, tacnodes, and ramphoid cusps, and use the aforementioned techniques to show that these stacks are weakly proper. This will be the key ingredient in forthcoming work, in which we will prove that these moduli stacks have projective good moduli spaces which are log canonical models for $\bar{M}_g$.

Author

Alper, Jarod; Smyth, David Ishii; van der Wyck, Frederick

Published

2010

Language

EN