Cohomology ring of the flag variety vs Chow cohomology ring of the Gelfand-Zetlin toric variety

2019/06/01 by Kaveh, Kiumars, Villella, Elise
#14C15 #14M25 #57T15 #Algebraic Geometry (math.AG) #FOS: Mathematics #Primary: 14M15 #Secondary: 52B20

paper · doi:10.48550/arxiv.1906.00154

Abstract

We compare the cohomology ring of the flag variety FL_n and the Chow cohomology ring of the Gelfand-Zetlin toric variety X_GZ. We show that H^*(FL_n, ℚ) is the Gorenstein quotient of the subalgebra L of A^*(X_GZ, ℚ) generated by degree 1 elements. We compute these algebras for n=3 to see that, in general, the subalgebra L does not have Poincare duality.

Related

• Chow-Witt rings and topology of flag varieties
• Functorial relationships between quantum cohomology of complete and partial flag varieties, (II)
• Some questions arising from the study of cohomology on flag varieties
• Gelfand-Tsetlin algebras and cohomology rings of Laumon spaces
• Equivariant cohomology of quaternionic flag manifolds