There has been much excitement in the recent literature about the idea that tensor network models, which construct states whose entanglement properties mimic those of CFT vacua, correspond geometrically to a bulk space one dimension higher. Such discrete models of holography tend to miss at least two interesting features of the continuum AdS/CFT correspondence: there, an essential ingredient is the group of isometries, which acts via conformal transformations of the boundary. Furthermore, the local data in tensor networks (a choice of a finite-rank tensor, which is taken to be "perfect" in one interesting class of models) is not obviously related to any dynamics that resemble field theory. I'll give a rather biased outsider's perspective on approaches to both of these issues, taking inspiration in each case from algebraic geometry.