Tate's algorithm and F-theory

Sheldon Katz, David R. Morrison, Sakura Schäfer-Nameki, James Sully

Research output: Contribution to journalArticlepeer-review


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.

Original languageEnglish (US)
Article number94
JournalJournal of High Energy Physics
Issue number8
StatePublished - 2011


  • D-branes
  • F-Theory

ASJC Scopus subject areas

  • Nuclear and High Energy Physics

Fingerprint Dive into the research topics of 'Tate's algorithm and F-theory'. Together they form a unique fingerprint.

Cite this