Kernels for Grassmann flops

Ballard, Matthew R.; Chidambaram, Nitin K.; Favero, David; McFaddin, Patrick K.; Vandermolen, Robert R.

doi:10.1016/j.matpur.2021.01.005

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Kernels for Grassmann flops

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Chidambaram, Nitin K.
Max Planck Institute for Mathematics, Max Planck Society;

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https://doi.org/10.1016/j.matpur.2021.01.005
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arXiv:1904.12195.pdf
(Preprint), 343KB

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Citation

Ballard, M. R., Chidambaram, N. K., Favero, D., McFaddin, P. K., & Vandermolen, R. R. (in press). Kernels for Grassmann flops. Journal de Mathématiques Pures et Appliquées, Corrected Proof Online - Print pending. doi:10.1016/j.matpur.2021.01.005.

Cite as: http://hdl.handle.net/21.11116/0000-0007-E838-5

Abstract

We develop a generalization of the $Q$-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.