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On the Strominger System and Holomorphic Deformations

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Abstract

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.

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Acknowledgements

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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Correspondence to Luis Ugarte.

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Ivanov, S., Ugarte, L. On the Strominger System and Holomorphic Deformations. J Geom Anal 29, 917–935 (2019). https://doi.org/10.1007/s12220-018-0023-5

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