Holomorphic quadratic differential
= Holomorphic quadratic differential
{title2=$q\in H^0(X,K_X^2)$}
A <quadratic differential> with <holomorphic> local coefficients. If it is nonzero, its zeros have total order $4g-4$ on a <compact> <genus>-$g$ <Riemann surface>. Away from its zeros, a nonzero differential has <flat coordinates> whose changes of coordinate have the form $w\mapsto\pm w+c$.