The Schubert flop derived-equivalence conjecture

Let YCl0,CY0l0,CYCY_{-C}\xleftarrow{\,l_{0,-C}\,}Y_0\xrightarrow{\,l_{0,C}\,}Y_C be the Schubert flop diagram for a one-dimensional face CC in the remaining case described in the paper. The maps induce the derived functors appearing below. Schubert flop derived-equivalence conjecture. The functor

R(l0,C)l0,C:Db(YC)Db(YC)R(l_{0,C})_*\circ l_{0,-C}^*:D^b(Y_{-C})\longrightarrow D^b(Y_C)

is a derived equivalence. The paper identifies this as the only remaining invertibility question for the stated sl3\mathfrak{sl}_3-flober conditions and plans to address it in future work.

Sources & referencesView supporting material

Primary source

Alexey Bondal, Mikhail Kapranov and Vadim Schechtman, “Perverse schobers and birational geometry”, arXiv:1801.08286 (2018).

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