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

Date created: 
2014-08-12
Identifier: 
etd8588
Keywords: 
Jacobian Variety
Decomposition
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 type: 
Thesis
Rights: 
Copyright remains with the author. The author granted permission for the file to be printed and for the text to be copied and pasted.
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Senior supervisor: 
Nils Bruin
Department: 
Science: Department of Mathematics
Thesis type: 
(Thesis) M.Sc.
Statistics: