Kernels for Grassmann Flops
arXiv:1904.12195 · doi:10.1016/j.matpur.2021.01.005
Abstract
We develop a generalization of the -construction of the first author, Diemer, and the third author for Grassmann flips. This generalization provides a canonical idempotent kernel on the derived category of the associated global quotient stack. The idempotent kernel, after restriction, induces a semi-orthogonal decomposition which compares the flipped varieties. Furthermore its image, after restriction to the geometric invariant theory semistable locus, "opens" a canonical "window" in the derived category of the quotient stack. We check this window coincides with the set of representations used by Kapranov to form a full exceptional collection on Grassmannians.
arXiv comment30 pages, expanded to identify the orthogonal for Grassmann flips, accepted for publication by Journal de Mathématiques Pures et Appliquées
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