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

Authors

  • Lino Grama University of Campinas.
  • Leonardo Soriani University of Campinas.

DOI:

https://doi.org/10.22199/issn.0717-6279-5481

Keywords:

generalized complex geometry, mirror symmetry, elliptic curves

Abstract

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.

Author Biographies

Lino Grama, University of Campinas.

Department of Mathematics, IMECC.

Leonardo Soriani, University of Campinas.

Department of Mathematics, IMECC

References

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

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G. Cavalcanti and M. Gualtieri, “Generalized complex geometry and T-duality”, in A celebration of the mathematical legacy of Raoul Bott, P. R. Kotiuga, Ed. Providece. RI: AMS, 2011.

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., 2008, pp. 95-166.

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, pp. 443-470, 1998. https://doi.org/10.4310/ATMP.1998.v2.n2.a9

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

Published

2023-03-27

How to Cite

[1]
L. Grama and L. Soriani, “A remark about mirror symmetry of elliptic curves and generalized complex geometry”, Proyecciones (Antofagasta, On line), vol. 42, no. 2, pp. 445-456, Mar. 2023.

Issue

Section

Artículos