Kernels for Grassmann Flops
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.
Cite
@article{arxiv.1904.12195,
title = {Kernels for Grassmann Flops},
author = {Matthew R. Ballard and Nitin K. Chidambaram and David Favero and Patrick K. McFaddin and Robert R. Vandermolen},
journal= {arXiv preprint arXiv:1904.12195},
year = {2021}
}
Comments
30 pages, expanded to identify the orthogonal for Grassmann flips, accepted for publication by Journal de Math\'ematiques Pures et Appliqu\'ees