2023/10/02 by Vladimiro Benedetti, Benedetti, Vladimiro, Daniele Faenzi +3 · 1 citation
Mathematics · #Homotopy and Cohomology in Algebraic Topology #Advanced Algebra and Geometry #Algebraic structures and combinatorial models
paper · pdf · doi:10.48550/arxiv.2310.01090
We construct a full exceptional Lefschetz collection on the spinor 15-fold consisting of a connected component of the space of orthogonal 6-dimensional subspaces of a 12-dimensional complex vector space, isotropic with respect of a fixed non-degenerate quadratic form. The collection is made of 2 twists of a 4-item block and 8 twists of a 3-item block, confirming a conjecture of Kuznetsov and Smirnov. We speculate that a similar collection might work for the Freudenthal E7-variety.