Toric morphisms and fibrations of toric Calabi-Yau hypersurfaces

Yi Hu, Chien Hao Liu, Shing Tung Yau

Research output: Contribution to journalArticle

13 Scopus citations

Abstract

Special fibrations of toric varieties have been used by physicists, e.g. the school of Candelas, to construct dual pairs in the study of Het/F-theory duality. Motivated by this, we investigate in this paper the details of toric morphisms between toric varieties. In particular, a complete toric description of fibers - both generic and non-generic -, image, and the flattening stratification of a toric morphism are given. Two examples are provided to illustrate the discussions. We then turn to the study of the restriction of a toric morphism to a toric hypersurface. The details of this can be understood by the various restrictions of a line bundle with a section that defines the hypersurface. These general toric geometry discussions give rise to a computational scheme for the details of a toric morphism and the induced fibration of toric hypersurfaces therein. We apply this scheme to study the family of complex 4-dimensional elliptic Calabi-Yau toric hypersurfaces that appear in a recent work of Braun-Candelas-dlOssa-Grassi. Some directions for future work are listed in the end.

Original languageEnglish (US)
Pages (from-to)457-505
Number of pages49
JournalAdvances in Theoretical and Mathematical Physics
Volume6
Issue number3
StatePublished - May 1 2002

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Keywords

  • Elliptic calabi-yau manifold
  • Fibration
  • Fibred calabi-yau manifold
  • Heterotic-string/F-theory duality
  • Primitive cone
  • Relative star
  • Toric calabi-yau hypersurface
  • Toric morphism

ASJC Scopus subject areas

  • Mathematics(all)
  • Physics and Astronomy(all)

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