Homological Algebra of Mirror Symmetry

Maxim Kontsevich
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Maxim Kontsevich: Max Planck Institut für Mathematik

A chapter in Proceedings of the International Congress of Mathematicians, 1995, pp 120-139 from Springer

Abstract: 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 $$\dim {H^p}(V,{\Omega ^q}) = \dim {H^{n - p}}(W,{\Omega ^q}).$$ d i m H p ( V , Ω ) = d i m H n - p ( W , Ω q ) . .

Date: 1995
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DOI: 10.1007/978-3-0348-9078-6_11

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