2025/07/23 by Daigo Ito, Ito, Daigo, Noah Olander +1
Agricultural and Biological Sciences · Business, Management and Accounting · #Advanced Scientific Research Methods #Algebraic Geometry (math.AG) #FOS: Mathematics #Optics and Image Analysis
paper · pdf · doi:10.48550/arxiv.2507.17681
openalex publication_date 2025/07/23 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.