Corpus ID: 119148952

Nonexistence of semiorthogonal decompositions and sections of the canonical bundle

@article{Kawatani2015NonexistenceOS,
  title={Nonexistence of semiorthogonal decompositions and sections of the canonical bundle},
  author={K. Kawatani and Shinnosuke Okawa},
  journal={arXiv: Algebraic Geometry},
  year={2015}
}
We investigate semiorthogonal decomposition(SOD)s of the derived category of coherent sheaves on a smooth proper variety. We prove that global/local sections of the canonical bundle give a strong constraint on the supports of objects in one of the semiorthogonal summands. We also show that SODs are rigid under the action of topologically trivial autoequivalences. As applications of these results, we prove the non-existence of non-trivial SODs for various minimal models. 
12 Citations

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