In Grassmannians, dimension 3 and codimension 3 classes are realizable by irreducible subvarieties exactly when b²≥ac, and in G(2,n) classes are realizable over Q exactly when their coefficients form a log-concave sequence with no internal zeros.
Coskun, Rigidity of Schubert classes in orthogonal Grassmannians, Israel J
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Realization of Cohomology Classes in Grassmannians
In Grassmannians, dimension 3 and codimension 3 classes are realizable by irreducible subvarieties exactly when b²≥ac, and in G(2,n) classes are realizable over Q exactly when their coefficients form a log-concave sequence with no internal zeros.