On the Strominger System and Holomorphic Deformations



We prove that the property of existence of solution to the Strominger system in dimension six is neither open nor closed under holomorphic deformations of the complex structure. These results are obtained both in the case of positive slope parameter as well as in the case of negative slope parameter in the anomaly cancellation equation.


Complex structure Holomorhic deformation Balanced Hermitian metric Strominger system 

Mathematics Subject Classification

Primary 32G05 Secondary 53C55 53C07 81T30 



This work has been partially supported by the projects MINECO (Spain) MTM2014-58616-P, Gobierno de Aragón/Fondo Social Europeo–Grupo Consolidado E15 Geometría, and by Fundación Bancaria Ibercaja–Fundación CAI–Universidad de Zaragoza, Programa de Estancias de Investigación, Contracts DH 12/3/12.12.2017 and Contract 80-10-33/2017 with the Sofia University “St.Kl.Ohridski.” S.I. thanks the University of Zaragoza for the support during his visit to the Department of Mathematics, and L.U. thanks the University of Sofia “St. Kl. Ohridski” for the hospitality and financial support provided while visiting the Faculty of Mathematics and Informatics. The authors wish to thank the referee for useful comments and suggestions.


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Authors and Affiliations

  1. 1.Faculty of Mathematics and InformaticsUniversity of Sofia “St. Kl. Ohridski”SofiaBulgaria
  2. 2.Institute of Mathematics and InformaticsBulgarian Academy of SciencesSofiaBulgaria
  3. 3.Departamento de Matemáticas - I.U.M.A.Universidad de ZaragozaZaragozaSpain

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