{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 $w\mapsto\pm w+c$.


Holomorphic quadratic differential

{title2=$q=\phi(z)\,dz^2$}
{wiki}

A section of the square of the <canonical bundle>, locally $q=\phi(z)\,dz^2$; its coefficient changes by the square of the coordinate <derivative>. A <holomorphic quadratic differential> has <holomorphic> coefficient, and its <flat metric of a quadratic differential> is $|q|^{1/2}$.


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 Incoming links: Quadratic differential