The small quantum cohomology of the Cayley Grassmannian
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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 nonnegative and deduce Golyshev’s conjecture [Formula: see text] 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.
2014 ◽
Vol DMTCS Proceedings vol. AT,...
(Proceedings)
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2005 ◽
Vol 16
(08)
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pp. 823-839
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2001 ◽
Vol 131
(3)
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pp. 459-472
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1999 ◽
Vol 351
(7)
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pp. 2695-2729
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2015 ◽
Vol 160
(2)
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pp. 353-377
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2019 ◽
Vol 19
(6)
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pp. 1889-1929
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