19 citations · 21 across the 4 of their papers we have counts for
4 papers
Brauer-Manin obstructions on degree 2 K3 surfaces
Patrick Corn, Masahiro Nakahara
We analyze the Brauer-Manin obstruction to rational points on the K3 surfaces over given by double covers of ramified over a diagonal sextic. After find…
Computation on Elliptic Curves with Complex Multiplication
Pete L. Clark, Patrick Corn, Alex Rice +1
We give the complete list of possible torsion subgroups of elliptic curves with complex multiplication over number fields of degree 1-13. Additionally we describe the algorithm use…
Tate-Shafarevich groups and K3 surfaces
Patrick Corn
Following (and elaborating on) a method of Logan and van Luijk, we exhibit explicit genus-2 curves whose Jacobians have nontrivial 2-torsion in their Tate-Shafarevich groups.
Del Pezzo surfaces of degree 6
Patrick Corn
We give a correspondence which associates, to any Del Pezzo surface X of degree 6 over a field k of characteristic 0, a collection of data consisting of a Severi-Brauer variety/k a…