The Geometry of Moduli Spaces of Maps from Curves

Author: Ye, Seunghee

Year: 2017

Degree: Dissertation (Ph.D.)

Advisor: Graber, Thomas B.

Committee Members: Graber, Thomas B.; Marcolli, Matilde; Solis, Pablo R.; Zhu, Xinwen

Option: Mathematics

DOI: 10.7907/Z9MP5191

Abstract

A class of moduli spaces that has long been the interest of many algebraic geometers is the class of moduli spaces parametrizing maps from curves to target spaces. Different such moduli spaces have distinct geometry and also invariants associated to them. In this thesis, we will study the geometry of three such moduli spaces. By understanding the global geometry of each moduli space, we will produce a stratification, which plays a central role in proving a result about invariants associated to the space.

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