• Corpus ID: 232404566

Fullness of exceptional collections via stability conditions -- A case study: the quadric threefold

@inproceedings{Bolognese2021FullnessOE,
  title={Fullness of exceptional collections via stability conditions -- A case study: the quadric threefold},
  author={Barbara Bolognese and Domenico Fiorenza},
  year={2021}
}

• Barbara Bolognese, D. Fiorenza
• Published 28 March 2021
• Mathematics

A powerful tool of investigation of Fano varieties is provided by exceptional collections in their derived categories. Proving the fullness of such a collection is generally a nontrvial problem, usually solved on a case-by-case basis, with the aid of a deep understanding of the underlying geometry. Likewise, when an exceptional collection is not full, it is not straightforward to determine whether its “residual” category, i.e., its right orthogonal, is the derived category of a variety. We show how one can use the existence of Bridgeland stability condition these residual categories (when they exist) to address these problems. We examine a simple case in detail: the quadric threefold Q3 in P. We also give an indication how a variety of other classical results could be justified or re-discovered via this technique., e.g., the commutativity of the Kuznetsov component of the Fano threefold Y4.