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Functional Analysis on the Eve of the 21st Century Volume II pp 301–323Cite as

A Note on ODEs from Mirror Symmetry

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Part of the book series: Progress in Mathematics ((PM,volume 132))

Abstract

We give close formulas for the counting functions of rational curves on complete intesection Calabi-Yau manifolds in terms of special solutions of generalized hypergeometric differential systems. For the one modulus cases we derive a differential equation for the Mirror map, which can be viewed as a generalization of the Schwarzian equation. We also derive a nonlinear seventh order differential equation which directly governs the Prepotential.

Research supported by grant DE-FG02-88-ER-25065

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Author information

Authors and Affiliations

  1. Theory Division, CERN, CH-1211, Geneva, 23, Switzerland

    A. Klemm

  2. Department of Mathematics, Harvard University, 02138, Cambridge, MA, USA

    B. H. Lian & S. T. Yau

  3. Institute of Mathematics, Academia Sinica, Taipei, Taiwan

    S. S. Roan

Authors
  1. A. Klemm
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  2. B. H. Lian
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  3. S. S. Roan
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  4. S. T. Yau
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Editor information

Editors and Affiliations

  1. Department of Mathematics, Rutgers University, 08903, New Brunswick, NJ, USA

    Simon Gindikin , James Lepowsky  & Robert L. Wilson ,  & 

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© 1996 Birkhäuser Boston

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Klemm, A., Lian, B.H., Roan, S.S., Yau, S.T. (1996). A Note on ODEs from Mirror Symmetry. In: Gindikin, S., Lepowsky, J., Wilson, R.L. (eds) Functional Analysis on the Eve of the 21st Century Volume II. Progress in Mathematics, vol 132. Birkhäuser Boston. https://doi.org/10.1007/978-1-4612-4098-3_4

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  • DOI: https://doi.org/10.1007/978-1-4612-4098-3_4

  • Publisher Name: Birkhäuser Boston

  • Print ISBN: 978-1-4612-8651-6

  • Online ISBN: 978-1-4612-4098-3

  • eBook Packages: Springer Book Archive

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