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Mirror Symmetry and Elliptic Curves

  • Conference paper
The Moduli Space of Curves

Part of the book series: Progress in Mathematics ((PM,volume 129))

Abstract

I review how recent results in quantum field theory confirm two general predictions of the mirror symmetry program in the special case of elliptic curves: (1) counting functions of holomorphic curves on a Calabi-Yau space (Gromov-Witten invariants) are ‘quasimodular forms’ for the mirror family; (2) they can be computed by a summation over trivalent Feynman graphs.

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Author information

Authors and Affiliations

  1. Department of Mathematics, University of Amsterdam, Plantage Muidergracht 24, 1018 TV, Amsterdam, The Netherlands

    Robbert Dijkgraaf

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  1. Robbert Dijkgraaf
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Editors and Affiliations

  1. Faculteit Wiskunde en Informatica, Universiteit van Amsterdam, 1018 TV, Amsterdam, The Netherlands

    Robbert H. Dijkgraaf , Carel F. Faber  & Gerard B. M. van der Geer ,  & 

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© 1995 Birkhäuser Boston

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Dijkgraaf, R. (1995). Mirror Symmetry and Elliptic Curves. In: Dijkgraaf, R.H., Faber, C.F., van der Geer, G.B.M. (eds) The Moduli Space of Curves. Progress in Mathematics, vol 129. Birkhäuser Boston. https://doi.org/10.1007/978-1-4612-4264-2_5

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  • DOI: https://doi.org/10.1007/978-1-4612-4264-2_5

  • Publisher Name: Birkhäuser Boston

  • Print ISBN: 978-1-4612-8714-8

  • Online ISBN: 978-1-4612-4264-2

  • eBook Packages: Springer Book Archive

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