2023/10/04 by Hiraku Abe, Abe, Hiraku, Haozhi Zeng +1 · 2 citations
Mathematics · #14M25 #Advanced Combinatorial Mathematics #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Algebraic structures and combinatorial models #FOS: Mathematics #primary: 14M15 #secondary: 57S12
paper · pdf · doi:10.48550/arxiv.2310.02818
openalex publication_date 2023/10/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The Peterson variety is a remarkable variety introduced by Dale Peterson to describe the quantum cohomology rings of all the partial flag varieties. The rational cohomology ring of the Peterson variety is known to be isomorphic to that of a particular toric orbifold which naturally arises from the given root system. In this paper, we show that it is not an accidental algebraic coincidence; we construct an explicit morphism from the Peterson variety to the toric orbifold which induces a ring isomorphism between their rational cohomology rings.