A derived category analogue of the Nakai--Moishezon criterion

Daigo Ito; Noah Olander

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arXiv · 2507.17681

A derived category analogue of the Nakai--Moishezon criterion

Daigo Ito·Noah Olander

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Abstract

We give a complete characterization of the line bundles on a proper variety whose tensor powers generate the derived category, answering a 2010 question of Chris Brav. The condition is analogous to the Nakai--Moishezon criterion and can be stated purely in terms of classical notions of positivity of line bundles. There is also a generalization which works for all Noetherian schemes. We use our criterion to prove basic properties of such line bundles and provide non-trivial examples of them. As an application, we give new examples of varieties which can be reconstructed from their derived categories in the sense of the Bondal--Orlov Reconstruction Theorem.

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Daigo Ito, Noah Olander. 2025-07-23. A derived category analogue of the Nakai--Moishezon criterion. https://arxiv.org/abs/2507.17681

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