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arXiv · 2505.13005

Full exceptional collections on the isotropic Grassmannians

Lyalya Guseva·Alexander Novikov
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Abstract

We prove that the Kuznetsov--Polishchuk exceptional collections on rational homogeneous spaces of the symplectic groups $\mathrm{Sp}(2n,\mathbb{C})$ 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.

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Lyalya Guseva, Alexander Novikov. 2025-05-19. Full exceptional collections on the isotropic Grassmannians. https://arxiv.org/abs/2505.13005

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