Mirror Symmetry and Toric Degenerations of Partial Flag Manifolds

Abstract

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 $P(n_1,...,n_l,n)$.

46 pages with 9 figures, LaTeX

References in corpus (1)

• A mirror theorem for toric complete intersections

Cited by in corpus (1)

• The making of Calabi-Yau spaces: Beyond toric hypersurfaces