= Canonical-form transition on projective space
{title2=$\omega_i=(-1)^i(X_i/X_0)^{-n-1}\omega_0$}
On the standard charts of <projective space>, wedge the coordinate differentials in increasing order. The change $X_0/X_i=(X_i/X_0)^{-1}$ and $X_j/X_i=(X_j/X_0)/(X_i/X_0)$ gives the displayed <Jacobian determinant>. Multiplying the $i$th local generator by $(-1)^i$ removes this sign and yields the transition functions of the <twisting sheaf on projective space> with degree $-n-1$.
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