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arXiv · 1906.00154

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

Kiumars Kaveh·Elise Villella
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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 $H^*(FL_n, \mathbb{Q})$ is the Gorenstein quotient of the subalgebra $L$ of $A^*(X_{GZ}, \mathbb{Q})$ 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.

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Kiumars Kaveh, Elise Villella. 2019-06-01. Cohomology ring of the flag variety vs Chow cohomology ring of the Gelfand-Zetlin toric variety. https://arxiv.org/abs/1906.00154

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