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Introduction to Homological Mirror Symmetry

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Superschool on Derived Categories and D-branes (SDCD 2016)

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Abstract

Mirror symmetry states that to every Calabi-Yau manifold \(X\) with complex structure and symplectic symplectic structure there is another dual manifold \(X^\vee \), so that the properties of \(X\) associated to the complex structure (e.g. periods, bounded derived category of coherent sheaves) reproduce properties of \(X^\vee \) associated to its symplectic structure (e.g. counts of pseudo holomorphic curves and discs).

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Notes

  1. 1.

    One can forget the condition that X be affine, though this comes at the cost of clarity.

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Author information

Authors and Affiliations

  1. Department of Mathematics, University of Miami, Coral Gables, FL, 33146, USA

    Andrew Harder

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  1. Andrew Harder
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Correspondence to Andrew Harder .

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Editors and Affiliations

  1. Department of Mathematics, University of South Carolina, Columbia, South Carolina, USA

    Matthew Ballard

  2. Department of Mathematics and Statistical Sciences, University of Alberta, Edmonton, Alberta, Canada

    Charles Doran

  3. Department of Mathematics and Statistical Sciences, University of Alberta, Edmonton, Alberta, Canada

    David Favero

  4. Department of Physics, Virginia Tech, Blacksburg, Virginia, USA

    Eric Sharpe

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Harder, A. (2018). Introduction to Homological Mirror Symmetry. In: Ballard, M., Doran, C., Favero, D., Sharpe, E. (eds) Superschool on Derived Categories and D-branes. SDCD 2016. Springer Proceedings in Mathematics & Statistics, vol 240. Springer, Cham. https://doi.org/10.1007/978-3-319-91626-2_12

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