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.
| Identifer | oai:union.ndltd.org:purdue.edu/oai:figshare.com:article/12743702 |
| Date | 30 July 2020 |
| Creators | Christopher E Creighton (9189347) |
| Source Sets | Purdue University |
| Detected Language | English |
| Type | Text, Thesis |
| Rights | CC BY 4.0 |
| Relation | https://figshare.com/articles/thesis/Automorphism_Groups_And_Chern_Bounds_of_Fibrations/12743702 |
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