6533b7d7fe1ef96bd12684eb
RESEARCH PRODUCT
Mirror symmetry and toric degenerations of partial flag manifolds
Bumsig KimIonuţ Ciocan-fontanineVictor V. BatyrevDuco Van Stratensubject
ConjectureMathematics::Commutative AlgebraGeneral MathematicsComplete intersectionFano varietyCombinatoricsMathematics - Algebraic GeometryMathematics::Algebraic GeometryFOS: MathematicsLocus (mathematics)Mirror symmetryAlgebraic Geometry (math.AG)Mathematics::Symplectic GeometryMathematicsdescription
In this paper we propose and discuss a mirror construction for complete intersections in partial flag manifolds $F(n_1, ..., n_l, n)$. This construction includes our previous mirror construction for complete intersection in Grassmannians and the mirror construction of Givental for complete flag manifolds. The key idea of our construction is a degeneration of $F(n_1, ..., n_l, n)$ to a certain Gorenstein toric Fano variety $P(n_1, ..., n_l, n)$ which has been investigated by Gonciulea and Lakshmibai. We describe a natural small crepant desingularization of $P(n_1, ..., n_l, n)$ and prove a generalized version of a conjecture of Gonciulea and Lakshmibai on the singular locus of $P(n_1, ..., n_l, n)$.
| year | journal | country | edition | language |
|---|---|---|---|---|
| 1998-03-23 |