The integral cohomology rings of Peterson varieties in type A

2022/03/05 by Hiraku Abe, Abe, Hiraku, Haozhi Zeng +1
Mathematics · #Commutative Algebra and Its Applications #Algebraic structures and combinatorial models #Algebraic Geometry and Number Theory

paper · pdf · doi:10.48550/arxiv.2203.02629

Abstract

In this paper, we study the ring structure of the integral cohomology of the Peterson variety of type A_n-1. We give two kinds of descriptions: (1) we show that it is isomorphic to the \mathfrakS_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.

Related

• Toward cohomology rings of intersections of Peterson varieties and Richardson varieties
• Geometry of Peterson Schubert calculus in type A and left-right diagrams
• Cohomology of type B real permutohedral varieties
• The cohomology rings of real permutohedral varieties
• Peterson varieties and toric orbifolds associated to Cartan matrices