Solubility of a family of conics with polynomial coefficients in many variables

Mathieu Da Silva

We study the proportion of conics given by $({\mathcal{C}}_{\mathbf{F},\mathbf{y}}):F_0(\mathbf{y})x_0^2+F_1(\mathbf{y})x_1^2=F_2(\mathbf{y})x_2^2$ which have a rational poi…