Cohomology of hyperplane sections of (co)adjoint varieties

2022/07/05 by Vladimiro Benedetti, Benedetti, Vladimiro, Nicolas Perrin-Gilbert +1 · 2 citations
Mathematics · #Advanced Combinatorial Mathematics #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Algebraic structures and combinatorial models #FOS: Mathematics #Representation Theory (math.RT)

paper · pdf · doi:10.48550/arxiv.2207.02089

openalex publication_date 2022/07/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper we study general hyperplane sections of adjoint and coadjoint varieties. We show that these are the only sections of homogeneous varieties such that a maximal torus of the automorphism group of the ambient variety stabilizes them. We then study their geometry, provide formulas for their classical cohomology rings in terms of Schubert classes and compute the quantum Chevalley formula. This allows us to obtain results about the semi-simplicity of the (small) quantum cohomology, analogous to those holding for (co)adjoint varieties.

Cited by

• A-D-E diagrams, Hodge--Tate hyperplane sections and semisimple quantum cohomology
• Motives of Certain Hyperplane Sections of Milnor Hypersurfaces

Related

• On the big quantum cohomology of coadjoint varieties
• A-D-E diagrams, Hodge--Tate hyperplane sections and semisimple quantum cohomology
• On the quantum cohomology of homogeneous varieties
• The quantum cohomology of homogeneous varieties
• Equivariant quantum cohomology of homogeneous spaces