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Homological Algebra of Mirror Symmetry

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Abstract

Mirror symmetry (MS) was discovered several years ago in string theory as a duality between families of 3-dimensional Calabi-Yau manifolds (more precisely, complex algebraic manifolds possessing holomorphic volume elements without zeros). The name comes from the symmetry among Hodge numbers. For dual Calabi-Yau manifolds V, W of dimension n (not necessarily equal to 3) one has

$$\dim {H^p}(V,{\Omega ^q}) = \dim {H^{n - p}}(W,{\Omega ^q}).$$

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Author information

Authors and Affiliations

  1. Max Planck Institut für Mathematik, Gottfried-Claren-Straße 26, Bonn, D-53225, Germany

    Maxim Kontsevich

  2. Mathematics Department, University of California, Berkeley, CA, 94720, USA

    Maxim Kontsevich

Authors
  1. Maxim Kontsevich
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Editor information

Editors and Affiliations

  1. Département de Mathématiques, EPFL, 1015, Laussane, Switzerland

    S. D. Chatterji

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© 1995 Birkhäser Verlag, Basel, Switzerland

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Kontsevich, M. (1995). Homological Algebra of Mirror Symmetry. In: Chatterji, S.D. (eds) Proceedings of the International Congress of Mathematicians. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-9078-6_11

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  • DOI: https://doi.org/10.1007/978-3-0348-9078-6_11

  • Publisher Name: Birkhäuser, Basel

  • Print ISBN: 978-3-0348-9897-3

  • Online ISBN: 978-3-0348-9078-6

  • eBook Packages: Springer Book Archive

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