Gaussian maps for double covers of smooth toric surfaces

Abstract

This dissertation will expand on the results in Duflot, Gaussian Maps for Double Coverings, (Manuscripta Mathematica 82, 1994), considering both double covers of smooth toric surfaces and Hirzebruch surfaces and going further to consider curves on double covers of Hirzebruch surfaces. Results specifically address surjectivity as well as computations of corank.