Tate’s algorithm and F-theory
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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 “Tateforms” (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.
- J. Tate, Algorithm for determining the type of a singular fiber in an elliptic pencil, in Modular functions of one variable, IV — Proc. Internat. Summer School, Univ. Antwerp, Antwerp, (1972), Lecture Notes in Math. 476, Springer, Berlin Germany (1975) 33.Google Scholar
- D.R. Morrison and W. Taylor, Matter and singularities, to appear.Google Scholar
- A. Grassi and D.R. Morrison, Anomalies and the Euler characteristic of elliptic Calabi-Yau threefolds, to appear.Google Scholar