The Schubert flop derived-equivalence conjecture

About 8 years old · traced to

Let Y−C← l0,−C Y0→ l0,C YCY_{-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(Y−C)⟶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.

References

Primary source

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

Progress summary

Never refreshed

Nothing recorded yet. Refresh searches the literature and the public web for attempts on this problem, and writes the first summary here.

Solutions 0

No solutions have been posted yet.