Flops with and without tilting

Wahei Hara (Kavli IPMU, University of Tokyo)

Friday 14th March 15:00-16:00 Maths 311B

Abstract

This talk produces examples of higher dimensional flops that satisfies the D-equivalence conjecture.
The class of simple flop, which was introduced by Kanemitsu as a generalisation of the Atiyah flop, are expected to have tilting bundles, and the first half of this talk explains some of them actually have tilting bundles and that we can use those tilting bundles to prove the D-equivalence.
I also explain why the class of simple flops is remarkable, by presenting the connection to the study of complete-intersection Calabi-Yau manifolds.
The second half of this talk gives an example of a flop where the D-equivalence holds but no tilting object exists.
This example shows the technique to prove the D-equivalence using tilting objects is not enough to solve the DK conjecture in general.
The second part depends on the joint works with Michael Wemyss.

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