Gross, Benedict H.Wang, Xiaoheng2013-10-082013-10-082013Wang, Xiaoheng. 2013. Pencils of quadrics and Jacobians of hyperelliptic curves. Doctoral dissertation, Harvard University.http://dissertations.umi.com/gsas.harvard:10761http://nrs.harvard.edu/urn-3:HUL.InstRepos:11156784Using 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.en-USMathematicsHyperelliptic curvesPencils of quadricsThesis or Dissertation2013-10-08