A categorical flop in dimension one
Abstract
In this note we observe that the categorical structure of a flop occurs for some well-known non-commutative resolutions of a nodal curve. We describe the flop-flop spherical twists, and give a geometric interpretation in terms of Landau--Ginzburg models. The resolutions are all weakly crepant but not strongly crepant, and we formulate an intermediate condition that distinguishes the smaller ones.
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