Pencils of quadrics and Jacobians of hyperelliptic curves
Contributors: Gross, Benedict H.; Gross, Benedict H.; Harris, Joseph D.; Poonen, Bjorn
Published: 2013
Language: eng
Description: 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.
Notes: Keywords: Hyperelliptic curves, Pencils of quadrics.

Thesis Ph.D. Harvard University 2013