Full rectangular Lefschetz collection conjecture for odd isotropic Grassmannians

Let \IGr(n,2n+1)\IGr(n,2n+1) denote the odd isotropic Grassmannian parametrizing nn-dimensional isotropic subspaces of a (2n+1)(2n+1)-dimensional vector space equipped with a nondegenerate skew-symmetric form. A rectangular Lefschetz exceptional collection is a Lefschetz exceptional collection whose blocks all have the same length. The full rectangular Lefschetz collection conjecture. The bounded derived category Db(\IGr(n,2n+1))D^b(\IGr(n,2n+1)) admits a full rectangular Lefschetz exceptional collection. This is presented as plausible based on the index and rank of the Grothendieck group; the source provides no resolution, so the conjecture remains open.

Sources & referencesView supporting material

Primary source

Anton Fonarev, “On the bounded derived category of IGr(3, 7)”, arXiv:1804.06946 (2018).

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