Derived categories of Fano threefolds
By Alexander Kuznetsov. 2008
82 citations recorded by the source corpus.
We consider the structure of the derived categories of coherent sheaves on Fano threefolds with Picard number 1 and describe a strange relation between derived categories of different threefolds. In the appendix we discuss how the ring of algebraic cycles of a smooth projective variety is related to the Grothendieck group of its derived category.
Subfields: Algebra and Number Theory, Geometry and Topology
View Paper: https://www.semanticscholar.org/paper/280589ce384ad44781b8863a540654755a8d8745
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In Algebra and Number Theory
- Yuri Prokhorov
- P. Stellari
- Constantin Shramov
- Arend Bayer
- Emanuele Macrì
- Mart'i Lahoz
- Alexander Kuznetsov
- Michael Usher
In Geometry and Topology
- Emanuele Macrì
- P. Stellari
- Arend Bayer
- Mart'i Lahoz
- Alexander Kuznetsov
- Yuri Prokhorov
- Constantin Shramov
- D. Huybrechts
Citations in the corpus
- Derived Categories View on Rationality Problems (2015, background): “of Fano 3-folds sitting in the same row of the table have very much in common. In fact they are equivalent for rows 1, 2, and 4, and are 12 expected to be deformation equivalent for rows 6 and 8 (see [K09a] for precise results and conjectures). We mention this relation in the third column of the tab”
- Stability conditions on Kuznetsov components (2017, background): “In the case of Fano threefolds, there are a number of unexpected equivalences (some conjectural) between Kuznetsov components of pairs of Fano threefolds of index one and two, see [Kuz09a] for the theory, and [KPS16]”
- Hilbert schemes of lines and conics and automorphism groups of Fano threefolds (2016, methodology): “ory of coherent sheaves on Xis denoted by Db(X), see [Kuz14] for a recent survey. The main goal of this section is to prove Theorem 2.3.5. Besides, we give more detailed proofs of some facts, used in [Kuz09]. As before, we use notation and conventions of x2.1. We start by recalling Mukai’s results t”
- Instanton bundles on Fano threefolds (2012, methodology): “Indeed, it follows easily from the description of the numerical Grothendieck group of the category BY , see [15].”