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(n1, ..., nl, 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(n1, ..., nl, n) to a certain Gorenstein toric Fano variety P(n1, ..., nl, n) which has been investigated by Gonciulea and Lakshmibai. We describe a natural small crepant desingularization of P(n1, ..., nl, n) and prove a generalized version of a conjecture of Gonciulea and Lakshmibai on the singular locus of P(n1, ..., nl, n).
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