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RESEARCH PRODUCT
Conifold Transitions and Mirror Symmetry for Calabi-Yau Complete Intersections in Grassmannians
Bumsig KimVictor V. BatyrevDuco Van StratenIonuţ Ciocan-fontaninesubject
High Energy Physics - TheoryNuclear and High Energy PhysicsInstantonPure mathematicsConifoldComplete intersectionFOS: Physical sciencesFano planeMathematics - Algebraic GeometryMathematics::Algebraic GeometryHigh Energy Physics - Theory (hep-th)FOS: MathematicsCalabi–Yau manifoldGravitational singularityMathematics::Differential GeometryMirror symmetryAlgebraic Geometry (math.AG)Mathematics::Symplectic GeometryQuantum cohomologyMathematicsdescription
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.
| year | journal | country | edition | language |
|---|---|---|---|---|
| 1997-10-19 |