On Jacobians of dimension 2g that decompose into Jacobians of dimension g

Resource type
Thesis type
(Thesis) M.Sc.
Date created
2014-08-12
Authors/Contributors
Abstract
In this thesis we describe a family of Jacobian varieties of non-hyperelliptic genus 2g curves that are isogenous to a product of Jacobians of genus g curves in a specific way. For any hyperelliptic genus g curve C we construct a 2-parameter family of hyperelliptic genus g curves H with J(H)[2] isomorphic to J(C)[2], and a generically non-hyperelliptic curve A such that there is an isogeny from J(C)  J(H) to J(A) whose kernel is the graph of the isomorphism taking J(H)[2] to J(C)[2]. This is accomplished by first showing that C can be considered as a subcover of a Galois cover of a P1 that has A and H naturally arising as subcovers and then showing the naturally occurring isogeny relations have the desired kernel. We also list some corollaries to the main result and provide a magma script to generate non-hyperelliptic genus 4 curves that have curious automorphism groups.
Document
Identifier
etd8588
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Scholarly level
Supervisor or Senior Supervisor
Thesis advisor: Bruin, Nils
Member of collection
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etd8588_AKulkarni.pdf 1.01 MB