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The integral cohomology rings of Peterson varieties in type A

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arxiv 2203.02629 v2 pith:TQZC4EY7 submitted 2022-03-05 math.AG math.AT

Hiraku Abe , Haozhi Zeng This is my paper · ORCID
classification math.AGmath.AT
keywords ringcohomologyintegralpetersonstructuretypevarietydescriptions
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abstract

In this paper, we study the ring structure of the integral cohomology of the Peterson variety of type $\text{A}_{n-1}$. We give two kinds of descriptions: (1) we show that it is isomorphic to the $\mathfrak{S}_n$-invariant subring of the integral cohomology ring of the permutohedral variety, (2) we determine the ring structure in terms of ring generators and their relations.

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  1. Mixed Eulerian numbers and beyond

    math.AG 2025-02 accept novelty 8.0 of 10

    First explicit formula for mixed Eulerian numbers, and proof that matroidal mixed Eulerian numbers determine Derksen's G-invariant.

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