  We study a holomorphic representation for spinfoams. The representation is
obtained via the Ashtekar-Lewandowski-Marolf-Mour\~ao-Thiemann coherent state
transform. We derive the expression of the 4d spinfoam vertex for Euclidean and
for Lorentzian gravity in the holomorphic representation. The advantage of this
representation rests on the fact that the variables used have a clear
interpretation in terms of a classical intrinsic and extrinsic geometry of
space. We show how the peakedness on the extrinsic geometry selects a single
exponential of the Regge action in the semiclassical large-scale asymptotics of
the spinfoam vertex.
