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Introduction to homological mirror symmetry. (English) Zbl 1405.14103

Ballard, Matthew (ed.) et al., Superschool on derived categories and D-branes, Edmonton, Canada, July 17–23, 2016. Cham: Springer; Vancouver: Pacific Institute for the Mathematical Sciences (ISBN 978-3-319-91625-5/hbk; 978-3-319-91626-2/ebook). Springer Proceedings in Mathematics & Statistics 240, 139-161 (2018).
Summary: 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).
For the entire collection see [Zbl 1402.18001].

MSC:

14J33 Mirror symmetry (algebro-geometric aspects)
14F05 Sheaves, derived categories of sheaves, etc. (MSC2010)
14-01 Introductory exposition (textbooks, tutorial papers, etc.) pertaining to algebraic geometry
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