Journal of Algebraic Geometry

Journal of Algebraic Geometry

Online ISSN 1534-7486; Print ISSN 1056-3911

   
 
 

 

Inducing stability conditions


Authors: Emanuele Macrì, Sukhendu Mehrotra and Paolo Stellari
Journal: J. Algebraic Geom. 18 (2009), 605-649
DOI: https://doi.org/10.1090/S1056-3911-09-00524-4
Published electronically: March 10, 2009
MathSciNet review: 2524593
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Abstract | References | Additional Information

Abstract: We study stability conditions induced by functors between triangulated categories. Given a finite group acting on a smooth projective variety, we prove that the subset of invariant stability conditions embeds as a closed submanifold into the stability manifold of the equivariant derived category. As an application, we examine stability conditions on Kummer and Enriques surfaces and we improve the derived version of the Torelli Theorem for the latter surfaces already present in the literature. We also study the relationship between stability conditions on projective spaces and those on their canonical bundles.


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Emanuele Macrì
Affiliation: Hausdorff Center for Mathematics, Mathematisches Institut, Universität Bonn, Beringstr. 1, 53115 Bonn, Germany
Address at time of publication: Department of Mathematics, University of Utah, 155 South 1400 East, Salt Lake City, Utah 84112-0090
Email: macri@math.uni-bonn.de {and} macri@mpim-bonn.mpg.de, macri@math.utah.edu

Sukhendu Mehrotra
Affiliation: Department of Mathematics and Statistics, University of Massachusetts- Amherst, 710 N. Pleasant Street, Amherst, Massachusetts 010003
Email: mehrotra@math.umass.edu

Paolo Stellari
Affiliation: Dipartimento di Matematica “F. Enriques”, Università degli Studi di Milano, Via Cesare Saldini 50, 20133 Milano, Italy
Email: paolo.stellari@unimi.it

DOI: https://doi.org/10.1090/S1056-3911-09-00524-4
Received by editor(s): April 29, 2007
Received by editor(s) in revised form: April 17, 2008
Published electronically: March 10, 2009

American Mathematical Society