What is Isocyanates, Curtius and Hofmann rearrangements?

An isocyanate is a compound $\ce{R-N=C=O}$. In the Curtius rearrangement an acyl azide loses dinitrogen on heating while the R group moves from carbon to nitrogen, giving an isocyanate; in the Hofmann rearrangement a primary amide treated with bromine and base gives the same isocyanate through an N-bromoamide. With water the isocyanate gives the amine $\ce{RNH2}$ and carbon dioxide; with an alcohol, a carbamate.