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Automorphism Groups And Chern Bounds of Fibrations

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posted on 30.07.2020 by Christopher E Creighton
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.

History

Degree Type

Doctor of Philosophy

Department

Mathematics

Campus location

West Lafayette

Advisor/Supervisor/Committee Chair

Donu Arapura

Additional Committee Member 2

Kenji Matsuki

Additional Committee Member 3

Jaroslaw Wlodarczyk

Additional Committee Member 4

Sai Kee Yeung

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