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arXiv · 1904.12195

Kernels for Grassmann Flops

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

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Matthew R. Ballard, Nitin K. Chidambaram, David Favero, Patrick K. McFaddin, Robert R. Vandermolen. 2019-04-27. Kernels for Grassmann Flops. https://doi.org/10.1016/j.matpur.2021.01.005

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