Conifold transitions and mirror symmetry for Calabi-Yau complete intersections in Grassmannians

Victor V. Batyrev, Ionuţ Ciocan-Fontanine, Bumsig Kim, Duco Van Straten

Research output: Contribution to journalArticlepeer-review

79 Scopus citations

Abstract

In this paper we show that conifold transitions between Calabi-Yau 3-folds can be used for the construction of mirror manifolds and for the computation of the instanton numbers of rational curves on complete intersection Calabi-Yau 3-folds in Grassmannians. Using a natural degeneration of Grassmannians G(k, n) to some Gorenstein toric Fano varieties P(k, n) with conifolds singularities which was recently described by Sturmfels, we suggest an explicit mirror construction for Calabi-Yau complete intersections X ⊂ G(k, n) of arbitrary dimension. Our mirror construction is consistent with the formula for the Lax operator conjectured by Eguchi, Hori and Xiong for gravitational quantum cohomology of Grassmannians.

Original languageEnglish (US)
Pages (from-to)640-666
Number of pages27
JournalNuclear Physics B
Volume514
Issue number3
DOIs
StatePublished - Mar 23 1998

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