Kernels for Grassmann flops. (English. French summary) Zbl 1468.14034

Summary: We develop a generalization of the \(Q\)-construction of the first author et al. [“Kernels from compactifications”, Preprint, arXiv:1710.01418] 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 M. M. Kapranov [Invent. Math. 92, No. 3, 479–508 (1988; Zbl 0651.18008)] to form a full exceptional collection on Grassmannians.


14F08 Derived categories of sheaves, dg categories, and related constructions in algebraic geometry
14E05 Rational and birational maps
14L24 Geometric invariant theory


Zbl 0651.18008
Full Text: DOI arXiv


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