|Date||Oct 13, 2015|
One way to study solutions of a diophantine equation is to force them to parametrize certain geometric object. In this talk, I will construct K3 surfaces from certain geometric configuration in the projective plane, which will enable us to parametrize the solutions by K3 surfaces. There are two main examples, and in each case the surfaces are equipped with lattice polarizations of rank 16 and 18, respectively. The degeneration of these K3 surfaces will be also studied.