Relative singular twisted Bondal–Orlov

A theorem of Bondal and Orlov states that a smooth projective variety with ample or anti-ample canonical bundle can be reconstructed from its derived category. Here we extend the original result in three directions: we allow Gorenstein singularities, we consider derived categories of twisted sheaves and work relatively over a base stack.

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A huge thanks goes to Michael Groechenig: the present work work grew out of our collaboration, in addition to uncountably many conversations regarding the results contained here. I also thank Ben Antieau for carefully reading a draft of this paper and for providing many useful comments and suggestions. A final thanks goes to an anonymous referee for providing helpful comments and corrections.

Received 5 December 2016

Accepted 16 January 2017

Published 5 July 2018