Pencils of quadrics and Jacobians of hyperelliptic curves

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Pencils of quadrics and Jacobians of hyperelliptic curves

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Title: Pencils of quadrics and Jacobians of hyperelliptic curves
Author: Wang, Xiaoheng
Citation: Wang, Xiaoheng. 2013. Pencils of quadrics and Jacobians of hyperelliptic curves. Doctoral dissertation, Harvard University.
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Abstract: Using pencils of quadrics, we study a construction of torsors of Jacobians of hyperelliptic curves twice of which is Pic^1. We then use this construction to study the arithmetic invariant theory of the actions of SO2n+1 and PSO2n+2 on self-adjoint operators and show how they facilitate in computing the average order of the 2-Selmer groups of Jacobians of hyperelliptic curves with a rational Weierstrass point, and the average order of the 2-Selmer groups of Jacobians of hyperelliptic curves with a rational non-Weierstrass point, over arbitrary number fields.
Terms of Use: This article is made available under the terms and conditions applicable to Other Posted Material, as set forth at http://nrs.harvard.edu/urn-3:HUL.InstRepos:dash.current.terms-of-use#LAA
Citable link to this page: http://nrs.harvard.edu/urn-3:HUL.InstRepos:11156784
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