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, Restriction varieties and the rigidity problem in Schubert varieties, equivariant cohomology and characteristic classes--IMPANGA 15, 49--95, EMS Ser
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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.