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The general fluctuations, in the form of vertex operators, for the type IIsuperstring in the pure spinor formalism are considered. We review theconstruction of these vertex operators in flat space-time. We then review thetype II superstrings in curved background in the pure spinor formalism tofinally construct the vertex operators on a generic type II supergravitybackground.

General fluctuations of the type II pure spinor string on curved backgrounds