Exceptional vector bundles on Grassmannians. (English. Russian original) Zbl 1319.14018

Fonarev, A. V.

Russ. Math. Surv. 69, No. 4, 768-770 (2014); translation from Usp. Mat. Nauk 69, No. 4, 189-190 (2014).

This short note is an announcement and very rough sketch of a proof of Conjecture 9.8 from A. Kuznetsov and A. Polishchuk [J. Eur. Math. Soc. (JEMS) 18, No. 3, 507–574 (2016; Zbl 1338.14021)], on the existence of some particular exceptional collections of vector bundles in bounded derived categories of coherent sheaves on Grassmannian varieties. A more complete and clear account is now available in the author’s paper [Proc. Steklov Inst. Math. 290, 11–25 (2015; Zbl 1376.14022); translation from Tr. Mat. Inst. Steklova 290, 18–33 (2015)].

Reviewer: Carl Mautner (Bonn)

MSC:

14F05	Sheaves, derived categories of sheaves, etc. (MSC2010)
14M15	Grassmannians, Schubert varieties, flag manifolds

Citations:

Zbl 1338.14021; Zbl 1376.14022