Semiorthogonal decompositions in algebraic geometry

Kuznetsov, Alexander

doi:10.48550/arxiv.1404.3143

Cited by 36 publications

(40 citation statements)

References 16 publications

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“…Background and motivation. The study of Kuznetsov components of derived categories of Fano varieties started with [BO95], and has seen a lot of recent interest, see e.g., [Kuz04,Kuz05,IKP14] for threefolds, and [Kuz10, AT14,Add16] for the cubic fourfold, as well as [Kuz09a,Kuz14,Kuz15] for surveys. The interest in them comes from various directions.…”

Section: Introductionmentioning

confidence: 99%

Stability conditions on Kuznetsov components

Bayer¹,

Lahoz²,

Macrì³

et al. 2017

Preprint

199

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We introduce a general method to induce Bridgeland stability conditions on semiorthogonal decompositions. In particular, we prove the existence of Bridgeland stability conditions on the Kuznetsov component of the derived category of many Fano threefolds (including all but one deformation type of Picard rank one), and of cubic fourfolds. As an application, in the appendix, written jointly with Xiaolei Zhao, we give a variant of the proof of the Torelli theorem for cubic fourfolds by Huybrechts and Rennemo.

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Section: Introductionmentioning

confidence: 99%

Stability conditions on Kuznetsov components

Bayer¹,

Lahoz²,

Macrì³

et al. 2017

Preprint

199

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“…This result underlies many examples of interesting semi-orthogonal decompositions in geometry -we refer to [Kuz07,Kuz14,Ren15,Tho15] for further explanations of and examples in the theory of HP duality.…”

Section: Introductionmentioning

confidence: 56%

The fundamental theorem of homological projective duality via variation of GIT stability

Rennemo¹

2017

Preprint

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We reprove Kuznetsov's "fundamental theorem of homological projective duality" using LG models and variation of GIT stability. This extends the validity of the theorem from smooth varieties to nice subcategories of smooth quotient stacks, and moreover shows that the line bundles polarising the varieties in HP duality do not have to be globally generated.The proof combines ideas from Kuznetsov's original proof with ideas from work of Ballard-Deliu-Favero-Isik-Katzarkov.

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“…For a wonderful and comprehensive overview of the theory on semiorthogonal decompositions and its relevance in algebraic geometry we refer to [14].…”

Section: Exceptional Collections and Semiorthogonal Decompositionsmentioning

confidence: 99%