Arithmetic Dynamics and Higher Direct Images
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Authors
Zotine, Alexandre
Date
2024-08-12
Type
thesis
Language
eng
Keyword
arithmetic dynamics , toric geometry , sheaf cohomology
Alternative Title
Abstract
This thesis consists of two separate papers. In the first, we prove the Kawaguchi--Silverman conjecture for projective bundles on elliptic curves, thereby completing the conjecture for all projective bundles over curves. Our approach is to use the transition functions of the bundles. This allows us to further prove the conjecture for projective split bundles over a smooth projective variety with finitely generated Mori cone.
In the second paper, we give an algorithm for computing higher direct images of line bundles for toric morphisms. The state-of-the-art prior to our work only allows for computation when the toric morphism is between a product of projective spaces. We provide a new combinatorial framework for computing sheaf cohomology using cell complexes. Our method for computing higher direct images makes use of this construction. The algorithm developed is implemented explicitly in the mathematical software Macaulay2.
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Queen's University's Thesis/Dissertation Non-Exclusive License for Deposit to QSpace and Library and Archives Canada
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Copying and Preserving Your Thesis
This publication is made available by the authority of the copyright owner solely for the purpose of private study and research and may not be copied or reproduced except as permitted by the copyright laws without written authority from the copyright owner.
Attribution-NoDerivatives 4.0 International
ProQuest PhD and Master's Theses International Dissemination Agreement
Intellectual Property Guidelines at Queen's University
Copying and Preserving Your Thesis
This publication is made available by the authority of the copyright owner solely for the purpose of private study and research and may not be copied or reproduced except as permitted by the copyright laws without written authority from the copyright owner.
Attribution-NoDerivatives 4.0 International