  A Steiner bundle is a vector bundle on projective space arising as the
cokernel of the map defined by a matrix of linear forms. These come up in
various geometric settings, and by now they are the subject of a considerable
literature. Starting with work of Dolgachev and Kapranov from 1993, several
authors have considered the question of whether one can recover from the bundle
the geometric data used to construct it. Here we prove such Torelli-type
statements for the tautological bundles associated to sufficiently positive
divisors on any very ample linear series. In an appendix, we give a new proof
of the result of Dolgachev-Kapranov.
