A remark about mirror symmetry of elliptic curves and generalized complex geometry

• Grama, Lino ^[1] ; Soriani, Leonardo ^[1]
  1. [1] University of Campinas.
• Localización: Proyecciones: Journal of Mathematics, ISSN 0716-0917, ISSN-e 0717-6279, Vol. 42, Nº. 2, 2023, págs. 445-456
• Idioma: inglés
• DOI: 10.22199/issn.0717-6279-5481
• Enlaces
  • Texto completo
• Resumen

  • In this short note we describe the isomorphism of generalized complex structure between T-dual manifolds introduced by Cavalcanti-Gualtieri, in the case of elliptic curves. We also compare this isomorphism with the mirror map for elliptic curves described by Polishchuk and Zaslow.

• Referencias bibliográficas
  • D. Auroux, “Special Lagrangian fibrations, Mirror symmetry and Calabi-Yau double covers”, Astérisque, vol. 321, pp. 99-128, 2008. https://doi.org/10.48550/arXiv.0803.2734
  • V. del Barco, L. Grama and L. Soriani, “T-duality on nilmanifolds”, Journal of High Energy Physics, vol. 153, 2018. https://doi.org/10.1007/JHEP05(2018)153
  • P. Bouwknegt, K. Hannabuss and V. Mathai, “T-duality for principal torus bundles”, Journal of High Energy Physics, vol. 2004, no. 03, 2004....
  • G. Cavalcanti and M. Gualtieri, “Generalized complex geometry and T-duality”, in A celebration of the mathematical legacy of Raoul Bott, P....
  • M. Gualtieri, “Generalized complex geometry”, Annals of mathematics, vol. 174, pp. 75-123, 2011. https://doi.org/10.4007/annals.2011.174.1.3
  • R. Hain, “Lectures on moduli spaces of elliptic curves”, in Transformation Groups and Moduli Spaces of Curves, L. Ji and S. T. Yau, Eds.,...
  • M. Kontsevich, “Homological algebra of mirror symmetry”, Proceedings of the International Mathematical Congress, pp. 120-139, 1994. https://doi.org/10.48550/arXiv.alg-geom/9411018
  • R. McLean, “Deformations of calibrated submanifolds”, Communications in analysis and geometry, 1996.
  • A. Polishchuk and E. Zaslow, “Categorical mirror symmetry: the elliptic curve”, Advances in Theoretical and Mathematical Physics, vol. 2,...
  • A. Strominger, S-T. Yau and E. Zaslow, “Mirror symmetry is T-duality”, Nuclear Physics B, vol. 479, pp. 243-259, 1996. https://doi.org/10.1016/0550-3213(96)00434-8