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 involving 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.
The space of stability conditions on abelian threefolds, and on some Calabi-Yau threefolds / A. Bayer, E. Macrì, P. Stellari. - In: INVENTIONES MATHEMATICAE. - ISSN 0020-9910. - 206:3(2016 Dec), pp. 869-933.
|Titolo:||The space of stability conditions on abelian threefolds, and on some Calabi-Yau threefolds|
|Parole Chiave:||18E30; Primary 14F05; Secondary 14J30|
|Settore Scientifico Disciplinare:||Settore MAT/03 - Geometria|
|Progetto:||Spazi di moduli e applicazioni. |
Geometria delle Varietà Algebriche
|Data di pubblicazione:||dic-2016|
|Digital Object Identifier (DOI):||http://dx.doi.org/10.1007/s00222-016-0665-5|
|Appare nelle tipologie:||01 - Articolo su periodico|
File in questo prodotto:
|Stellari_InventionesMathematicae_SpaceStability_2016.pdf||Publisher's version/PDF||Open Access Visualizza/Apri|