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Explicit geometric and arithmetic properties of curves

Abstract : Algebraic curves are central objects in algebraic geometry. In this thesis, we consider these objects from different angles in algebraic geometry such as computational algebraic geometry and arithmetic geometry. In the first chapter, we study non-hyperelliptic curves of genus g and their Jacobians linked via theta characteristic divisors. Such divisors provide extrinsic geometric properties which allow us to compute theta constants. In the second chapter, we focus on hyperelliptic curves of genus 2 and the associated Kummer surface with a cryptographic motivation. In the third and final chapter, we examine unramified double covers of non-hyperelliptic curves of genus g to obtain information about the p-rank.
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Contributor : Türkü Özlüm Çelik Connect in order to contact the contributor
Submitted on : Monday, September 10, 2018 - 7:56:51 PM
Last modification on : Friday, May 20, 2022 - 9:04:50 AM
Long-term archiving on: : Tuesday, December 11, 2018 - 4:49:09 PM


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  • HAL Id : tel-01871465, version 1


Turku Ozlum Celik. Explicit geometric and arithmetic properties of curves. Algebraic Geometry [math.AG]. Universite Rennes 1, 2018. English. ⟨tel-01871465⟩



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