Multiview geometry is the study of two-dimensional images of three-dimensional scenes, a foundational subject in computer vision. We determine a universal Gröbner basis for the multiview ideal of   $n$  generic cameras. As the cameras move, the multiview varieties vary in a family of dimension
 $n$  generic cameras. As the cameras move, the multiview varieties vary in a family of dimension   $11n\,-\,15$ . This family is the distinguished component of a multigraded Hilbert scheme with a unique Borel-fixed point. We present a combinatorial study of ideals lying on that Hilbert scheme.
 $11n\,-\,15$ . This family is the distinguished component of a multigraded Hilbert scheme with a unique Borel-fixed point. We present a combinatorial study of ideals lying on that Hilbert scheme.