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Article Dans Une Revue International Journal of Mathematics Année : 2020

The small quantum cohomology of the Cayley Grassmannian

Vladimiro Benedetti
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Résumé

We compute the small cohomology ring of the Cayley Grassmannian, that parametrizes four-dimensional subalgebras of the complexified octonions. We show that all the Gromov-Witten invariants in the multiplication table of the Schubert classes are non negative and deduce Golyshev's conjecture O holds true for this variety. We also check that the quantum cohomology is semisimple and that there exists, as predicted by Dubrovin's conjecture, an exceptional collection of maximal length in the derived category.
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Dates et versions

hal-02184867 , version 1 (16-07-2019)

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Vladimiro Benedetti, Laurent Manivel. The small quantum cohomology of the Cayley Grassmannian. International Journal of Mathematics, 2020, 3. ⟨hal-02184867⟩
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