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Journal Article

On quantum cohomology of Grassmannians of isotropic lines, unfoldings An-singularities, and Lefschetz exceptional collections

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Cruz Morales,  John Alexander
Max Planck Institute for Mathematics, Max Planck Society;

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Smirnov,  Maxim
Max Planck Institute for Mathematics, Max Planck Society;

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http://aif.centre-mersenne.org/item/AIF_2019__69_3_955_0
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Citation

Cruz Morales, J. A., Kuznetsov, A., Mellit, A., Perrin, N., & Smirnov, M. (2019). On quantum cohomology of Grassmannians of isotropic lines, unfoldings An-singularities, and Lefschetz exceptional collections. Annales de l'Institut Fourier, 69(3), 955-991. Retrieved from http://arxiv.org/abs/1705.01819.


Cite as: https://hdl.handle.net/21.11116/0000-0004-8F97-1
Abstract
The subject of this paper is the big quantum cohomology rings of symplectic isotropic Grassmannians $\text{IG}(2, 2n)$. We show that these rings are regular. In particular, by "generic smoothness", we obtain a conceptual proof of generic semisimplicity of the big quantum cohomology for $\text{IG}(2, 2n)$.
Further, by a general result of Claus Hertling, the regularity of these rings implies that they have a description in terms of isolated hypersurface singularities, which we show in this case to be of type $A_{n-1}$. By the homological mirror symmetry conjecture, these results suggest the existence of a very special full exceptional collection in the derived category of coherent sheaves on $\text{IG}(2, 2n)$. Such a collection is constructed in the appendix by Alexander Kuznetsov.