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arXiv · 1802.08097

On residual categories for Grassmannians

Alexander Kuznetsov·Maxim Smirnov
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Abstract

We define and discuss some general properties of residual categories of Lefschetz decompositions in triangulated categories. In the case of the derived category of coherent sheaves on the Grassmannian $\text{G}(k,n)$ we conjecture that the residual category associated with Fonarev's Lefschetz exceptional collection is generated by a completely orthogonal exceptional collection. We prove this conjecture for $k = p$, a prime number, modulo completeness of Fonarev's collection (and for $p = 3$ we check this completeness).

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Alexander Kuznetsov, Maxim Smirnov. 2018-02-22. On residual categories for Grassmannians. https://doi.org/10.1112/plms.12294

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