  We apply exceptional generalised geometry to the study of exactly marginal
deformations of $\mathcal{N}=1$ SCFTs that are dual to generic AdS$_5$ flux
backgrounds in type IIB or eleven-dimensional supergravity. In the gauge
theory, marginal deformations are parametrised by the space of chiral primary
operators of conformal dimension three, while exactly marginal deformations
correspond to quotienting this space by the complexified global symmetry group.
We show how the supergravity analysis gives a geometric interpretation of the
gauge theory results. The marginal deformations arise from deformations of
generalised structures that solve moment maps for the generalised
diffeomorphism group and have the correct charge under the generalised Reeb
vector, generating the R-symmetry. If this is the only symmetry of the
background, all marginal deformations are exactly marginal. If the background
possesses extra isometries, there are obstructions that come from fixed points
of the moment maps. The exactly marginal deformations are then given by a
further quotient by these extra isometries.
  Our analysis holds for any $\mathcal{N}=2$ AdS$_5$ flux background. Focussing
on the particular case of type IIB Sasaki-Einstein backgrounds we recover the
result that marginal deformations correspond to perturbing the solution by
three-form flux at first order. In various explicit examples, we show that our
expression for the three-form flux matches those in the literature and the
obstruction conditions match the one-loop beta functions of the dual SCFT.
