What is the effective 2-form corresponding to the equation


$det Hess v=(v-q\_1v\_{q\_1}-q\_2v\_{q\_2})^4$


you can find the definition of effective forms [here](http://matematicas.uniandes.edu.co/~mikarm/TALLER_7/pdf/kushner.pdf)



finding effective 2-form corresponding to  an equation
Unless I'm mistaken, all the second derivatives of $v$ are isolated in the Hessian on the left-hand side. The notes you linked to already give the effective form that generates the Hessian. To get the effective form on for the right-hand side, simply multiply by $dq\_1 \wedge dq\_2$. So, I believe, the effective form you are looking for is
$$ dp\_1 \wedge dp\_2 - (v-q\_1 p\_1-q\_2 p\_2)^4 dq\_1\wedge dq\_2 . $$


