Automorphism Groups and Chern Bounds of Fibrations
Abstract
In this thesis, I study two problems. First, I generalize a result by H-Y Chen [1] to show that if X is a smooth variety of general type and irregularity q ≥ 1 that embeds into its Albanese variety as a smooth variety Y of general type with codimension one or two, then :Aut(X): ≤ :Aut(Fmin)::Aut(Y ): where Fmin 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
Ph.D.
Advisors
Arapura, Purdue University.
Subject Area
Civil engineering
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