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Mirror Symmetry and Toric Degenerations of Partial Flag Manifolds

Victor V. Batyrev·Ionut Ciocan-Fontanine·Bumsig Kim·Duco van Straten
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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 $P(n_1, ..., n_l, n)$.

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Victor V. Batyrev, Ionut Ciocan-Fontanine, Bumsig Kim, Duco van Straten. 1998-03-24. Mirror Symmetry and Toric Degenerations of Partial Flag Manifolds. https://arxiv.org/abs/math/9803108

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