Stability conditions on threefolds with nef tangent bundles

Koseki, Naoki

doi:10.48550/arxiv.1811.03267

Cited by 3 publications

(3 citation statements)

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“…Recently, the case of the quintic threefolds has finally been settled in [Li18]. For other cases with higher Picard rank, we refer to [BMSZ17,Piy17,Kos18a,Kos18b]. Unfortunately, the inequality does not hold in general, at least for higher Picard rank, see [Sch17], as well as [Kos18a, Appendix A] and [MS17].…”

Section: Bridgeland Stability In Families Ofmentioning

confidence: 99%

Stability conditions in families

Bayer,

Lahoz,

Macrì

et al. 2019

Preprint

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We develop a theory of Bridgeland stability conditions and moduli spaces of semistable objects for a family of varieties. Our approach is based on and generalizes previous work by Abramovich-Polishchuk, Kuznetsov, Lieblich, and Piyaratne-Toda. Our notion includes openness of stability, semistable reduction, a support property uniformly across the family, and boundedness of semistable objects. We show that such a structure exists whenever stability conditions are known to exist on the fibers.Our main application is the generalization of Mukai's theory for moduli spaces of semistable sheaves on K3 surfaces to moduli spaces of Bridgeland semistable objects in the Kuznetsov component associated to a cubic fourfold. This leads to the extension of theorems by Addington-Thomas and Huybrechts on the derived category of special cubic fourfolds, to a new proof of the integral Hodge conjecture, and to the construction of an infinite series of unirational locally complete families of polarized hyperkähler manifolds of K3 type.Other applications include the deformation-invariance of Donaldson-Thomas invariants counting Bridgeland stable objects on Calabi-Yau threefolds, and a method for constructing stability conditions on threefolds via degeneration.

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Section: Bridgeland Stability In Families Ofmentioning

confidence: 99%

Stability conditions in families

Bayer,

Lahoz,

Macrì

et al. 2019

Preprint

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“…a Kummer threefold [BMS16], or a product of an abelian variety and P n [Ko18a], • X with nef tangent bundle [Ko18b], and • X is a quintic threefold and (b, w) are described below [Li19b].…”

Section: Bogomolov-gieseker Inequalitymentioning

confidence: 99%

An application of wall-crossing to Noether-Lefschetz loci

Feyzbakhsh¹,

Thomas²

2019

Preprint

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Consider a smooth projective 3-fold X satisfying the Bogomolov-Gieseker conjecture of Bayer-Macrì-Toda (such as P 3 , the quintic threefold or an abelian threefold).Let L be a line bundle supported on a very positive surface in X. If c1(L) is a primitive cohomology class then we show it has very negative square.1 D may be singular. The results also apply to D reducible, so long as L is slope semistable on D.

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“…Stability conditions and moduli spaces also exist in the relative setting ([BLM + 19]). Finally, the existence of stability conditions is now known in interesting examples, including surfaces ( [Bri08,AB13]), certain Calabi-Yau threefolds ([MP15, BMS16,Li19b]), Fano threefolds ([Mac14, Sch14, Li19a, Piy17, BMSZ17]), some product varieties ( [Kos18a,Liu19]), and varieties with nef tangent bundles ( [Kos18b]). We review the definition and basic properties of Bridgeland stability conditions in Section 2.…”

Section: Introductionmentioning

confidence: 99%

Stability and Applications

Macrì,

Schmidt

2020

Preprint

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Stability conditions on threefolds with nef tangent bundles

Abstract: In this paper, we prove the Bogomolov-Gieseker type inequality conjecture for threefolds with nef tangent bundles. As a corollary, there exist Bridgeland stability conditions on these threefolds.

Cited by 3 publications

References 30 publications

Stability conditions in families

Stability conditions in families

An application of wall-crossing to Noether-Lefschetz loci

Stability and Applications

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