Journal
INTERNATIONAL JOURNAL OF MATHEMATICS
Volume 31, Issue 3, Pages -Publisher
WORLD SCIENTIFIC PUBL CO PTE LTD
DOI: 10.1142/S0129167X20500196
Keywords
Quasi homogeneous varieties; quantum cohomology; Dubrovin's conjecture
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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 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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