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

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

J. Math. Pures Appl. (9) 147, 29-59 (2021).

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.

MSC:

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

Keywords:

derived categories; birational geometry; representation theory

Citations:

Zbl 0651.18008

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