Conifold Transitions and Mirror Symmetry for Calabi-Yau Complete Intersections in Grassmannians

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 $X\subset G(k,n)$ 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.

36 pages, LaTeX 2.09

References in corpus (1)

• Rational Curves on the Space of Determinantal Nets of Conics

Cited by in corpus (32)

• Elliptic genera of 2d N=2 gauge theories
• Aspects of Non-Abelian Gauge Dynamics in Two-Dimensional N=(2,2) Theories
• Topological String Amplitudes, Complete Intersection Calabi-Yau Spaces and Threshold Corrections
• The equivariant A-twist and gauged linear sigma models on the two-sphere
• Minkowski Polynomials and Mutations
• Nonabelian 2D Gauge Theories for Determinantal Calabi-Yau Varieties
• GLSM's for partial flag manifolds
• A New Construction of Calabi-Yau Manifolds: Generalized CICYs
• Geometric Transitions
• Algorithms for minimal Picard-Fuchs operators of Feynman integrals
• Exact Kahler Potential for Calabi-Yau Fourfolds
• Quantum periods of Calabi-Yau fourfolds
• Thraxions: Ultralight Throat Axions
• Maximally Mutable Laurent Polynomials
• Geometric transitions between Calabi-Yau threefolds related to Kustin-Miller unprojections
• Thraxions: Towards Full String Models
• Four-dimensional Fano toric complete intersections
• Wilson loop algebras and quantum K-theory for Grassmannians
• Conifold transitions via affine geometry and mirror symmetry
• A categorification of U_T sl(1,1) and its tensor product representations
• Hodge Theory and Deformations of Affine Cones of Subcanonical Projective Varieties
• Quantum Periods For Certain Four-Dimensional Fano Manifolds
• Minuscule Schubert Varieties and Mirror Symmetry
• Prepotentials, Bi-linear Forms on Periods and Enhanced Gauge Symmetries in Type-II Strings
• Movable vs Monodromy Nilpotent Cones of Calabi-Yau Manifolds
• Equivariant A-twisted GLSM and Gromov--Witten invariants of CY 3-folds in Grassmannians
• Schubert calculus and singularity theory
• The making of Calabi-Yau spaces: Beyond toric hypersurfaces
• Determinantal Calabi-Yau varieties in Grassmannians and the Givental $I$-functions
• Singular symplectic spaces and holomorphic membranes
• Mutations of Fake Weighted Projective Spaces
• Mutation equivalence of toric Landau-Ginzburg models