Quantum cohomology of the odd symplectic Grassmannian of lines

2010/12/20 by Clélia Pech, Pech, Clélia · 1 citation
Mathematics · #Advanced Combinatorial Mathematics #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Geometry and complex manifolds #math.AG

paper · pdf · doi:10.48550/arxiv.1012.4257

25 pages, proof in section 2.1 simplified, proof of the existence of a full exceptional collection for the derived category IG(2,2n+1) added

openalex publication_date 2010/12/20 · arxiv created 2012/01/04 · arxiv updated 2012/01/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Odd symplectic Grassmannians are a generalization of symplectic Grassmannians to odd-dimensional spaces. Here we compute the classical and quantum cohomology of the odd symplectic Grassmannian of lines. Although these varieties are non homogeneous, we obtain Pieri and Giambelli formulas that are very similar to the symplectic case. We notice that their quantum cohomology is semi-simple, which enables us to check Dubrovin's conjecture for this case.

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• A-D-E diagrams, Hodge--Tate hyperplane sections and semisimple quantum cohomology

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