  The "Tate forms" for elliptically fibered Calabi-Yau manifolds are
reconsidered in order to determine their general validity. We point out that
there were some implicit assumptions made in the original derivation of these
"Tate forms" from the Tate algorithm. By a careful analysis of the Tate
algorithm itself, we deduce that the "Tate forms" (without any futher
divisiblity assumptions) do not hold in some instances and have to be replaced
by a new type of ansatz. Furthermore, we give examples in which the existence
of a "Tate form" can be globally obstructed, i.e., the change of coordinates
does not extend globally to sections of the entire base of the elliptic
fibration. These results have implications both for model-building and for the
exploration of the landscape of F-theory vacua.
