Creighton_Thesis.pdf (249.93 kB)

Automorphism Groups And Chern Bounds of Fibrations

thesis
posted on 30.07.2020, 23:02
In this thesis, I study two problems. First, I generalize a result by H-Y Chen to show that if $X$ is a smooth variety of general type and irregularity $q\geq 1$ that embeds into its Albanese variety as a smooth variety $Y$ of general type with codimension one or two, then $|Aut(X)|\leq |Aut(F_{min})||Aut(Y)|$ where $F_{min}$ is the minimal model of a general fiber. Then I describe a special type of fibration called a K-Fibration as a generalization to Kodaira Fibrations where we can compute its Chern numbers in dimensions 2 and 3. K-Fibrations act as an initial step in constructing examples of varieties that satisfy the generalization with the goal of computing their automorphism group explicitly.

Degree Type

Doctor of Philosophy

Mathematics

Campus location

West Lafayette

Donu Arapura

Kenji Matsuki

Jaroslaw Wlodarczyk