Homological Algebra of Mirror Symmetry

  title={Homological Algebra of Mirror Symmetry},
  author={Maxim Kontsevich},
  journal={arXiv: Algebraic Geometry},
  • M. Kontsevich
  • Published 1995
  • Mathematics, Physics
  • arXiv: Algebraic Geometry
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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