Inducing stability conditions

Macrì, Emanuele; Mehrotra, Sukhendu; Stellari, Paolo

doi:10.1090/s1056-3911-09-00524-4

Cited by 30 publications

(40 citation statements)

References 49 publications

(161 reference statements)

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“…Let X be a projective threefold with an action of a finite group G. In this section, we recall the main result of [28], which induces stability conditions on the G-equivariant derived category from G-invariant stability conditions on X ; similar results are due to Polishchuk, see [35,Sect. 2.2].…”

Section: The Space Of Stability Conditions On Some Calabi-yau Threefoldsmentioning

confidence: 99%

The space of stability conditions on abelian threefolds, and on some Calabi-Yau threefolds

2016

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We describe a connected component of the space of stability conditions on abelian threefolds, and on Calabi-Yau threefolds obtained as (the crepant resolution of) a finite quotient of an abelian threefold. Our proof includes the following essential steps:1. We simultaneously strengthen a conjecture by the first two authors and Toda, and prove that it follows from a more natural and seemingly weaker statement. This conjecture is a Bogomolov-Gieseker type inequality involv- ing the third Chern character of "tilt-stable" two-term complexes on smooth projective threefolds; we extend it from complexes of tilt-slope zero to arbitrary tilt-slope. 2. We show that this stronger conjecture implies the so-called support property of Bridgeland stability conditions, and the existence of an explicit open subset of the space of stability conditions. 3. We prove our conjecture for abelian threefolds, thereby reproving and generalizing a result by Maciocia and Piyaratne.Important in our approach is a more systematic understanding on the behaviour of quadratic inequalities for semistable objects under wall-crossing, closely related to the support property.

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Section: The Space Of Stability Conditions On Some Calabi-yau Threefoldsmentioning

confidence: 99%

The space of stability conditions on abelian threefolds, and on some Calabi-Yau threefolds

2016

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“…Macrì, Mehrotra and Stellari [26] studied the space of stability conditions on Kummer and Enriques surfaces. For arbitrary smooth projective surfaces, stability conditions have recently been constructed by Arcara and Bertram [1].…”

Section: Examples Of Stability Conditionsmentioning

confidence: 99%

Polynomial Bridgeland stability conditions and the large volume limit

Bayer

2009

Geom. Topol.

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We introduce the notion of a polynomial stability condition, generalizing Bridgeland stability conditions on triangulated categories. We construct and study a family of polynomial stability conditions for any normal projective variety. This family includes both Simpson-stability and large volume limits of Bridgeland stability conditions. We show that the PT/DT-correspondence relating stable pairs to Donaldson-Thomas invariants (conjectured by Pandharipande and Thomas) can be understood as a wallcrossing in our family of polynomial stability conditions. Similarly, we show that the relation between stable pairs and invariants of one-dimensional torsion sheaves (proven recently by the same authors) is a wall-crossing formula.

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“…This yields a natural equivalence between the bounded derived categories D b (Y ) and D b i * ( Y ). In [16], the authors described stability conditions on Enriques surfaces using i * -invariant stability conditions on Stab † ( Y ) via the functors π * and π * . Nuer [20] established the existence of projective coarse moduli spaces for Bridgeland stability conditions on Enriques surfaces.…”

Section: Moduli Spaces Of Stable Objects On K3 and Enriques Surfacesmentioning

confidence: 99%

“…. By the work of Macrì, Mehrotra, and Stellari [16] we know that the action of the covering involution i * is trivial on Stab † ( Y ). This yields…”

Section: Wall-crossing For Generic Enriques Surfaces Recall That We mentioning

confidence: 99%

Birational geometry of moduli spaces of stable objects on Enriques surfaces

Thorsten

2020

Sel. Math. New Ser.

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Using wall-crossing for K3 surfaces, we establish birational equivalence of moduli spaces of stable objects on generic Enriques surfaces for different stability conditions. As an application, we prove in the case of a Mukai vector of odd rank that they are birational to Hilbert schemes and that under an extra assumption every minimal model can be described as a moduli space. The argument makes use of a new Chow-theoretic result, showing that moduli spaces on an Enriques surface give rise to constant cycle subvarieties of the moduli spaces of the covering K3.

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Inducing stability conditions

Cited by 30 publications

References 49 publications

The space of stability conditions on abelian threefolds, and on some Calabi-Yau threefolds

The space of stability conditions on abelian threefolds, and on some Calabi-Yau threefolds

Polynomial Bridgeland stability conditions and the large volume limit

Birational geometry of moduli spaces of stable objects on Enriques surfaces

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