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Daniel Bragg, University of Utah


Title: Murphy’s Law for the moduli stack of curves


Abstract: Murphy's Law states "Anything that can go wrong will go wrong". In the context of algebraic geometry, "Murphy's Law" is used to refer to the philosophy that moduli spaces of algebro-geometric objects should be expected to have arbitrarily complicated structure, absent a good a-priori reason to think otherwise. In this talk I will explain my work verifying that a certain precise formulation of this philosophy holds for the moduli of curves, as well as a number of other natural moduli problems. This implies that the moduli space of curves fails to be a fine moduli space in every possible way, and that there exist curves which are obstructed from being defined over their fields of moduli by every possible mechanism. This is joint work with Max Lieblich.

 

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