Full exceptional collections on the isotropic Grassmannians

2025/05/19 by Lyalya Guseva, Alexander Novikov, Guseva, Lyalya +1
Mathematics · #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #FOS: Mathematics #Geometry and complex manifolds #Homotopy and Cohomology in Algebraic Topology #Representation Theory (math.RT)

paper · pdf · doi:10.48550/arxiv.2505.13005

openalex publication_date 2025/05/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We prove that the Kuznetsov--Polishchuk exceptional collections on rational homogeneous spaces of the symplectic groups Sp(2n,ℂ) are full and consist of vector bundles. To achieve this, we construct several classes of complexes, which we call generalized staircase complexes, symplectic staircase complexes and secondary staircase complexes -- each of which may be of independent interest.

Citations

• Secondary staircase complexes on isotropic Grassmannians
• Highest weight category structures on rep(B) and full exceptional collections on generalized flag varieties over \mathbb Z
• Derived category of the spinor 15-fold
• On the derived category of IGr(3, 9)
• On the derived category of the adjoint Grassmannian of type F
• Full exceptional collections on Lagrangian Grassmannians
• On the derived category of the Cayley plane II

Related

• Secondary staircase complexes on isotropic Grassmannians
• Dual exceptional collections on Lagrangian Grassmannians
• Full exceptional collections on the Lagrangian Grassmannians LG(4,8) and LG(5,10)
• On the derived category of the Cayley plane II
• Full exceptional collections on Lagrangian Grassmannians