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Fano versus Calabi - Yau | | Andrey N. Tyurin
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10 Feb 2003 | | Subject: | Algebraic Geometry | math.AG | | Abstract: | In this article we discuss some numerical parts of the mirror conjecture. For any 3 - dimensional Calabi - Yau manifold author introduces a generalization of the Casson invariant known in 3 - dimensional geometry, which is called Casson - Donaldson invariant. In the framework of the mirror relationship it corresponds to the number of SpLag cycles which are Bohr - Sommerfeld with respect to the given polarization. To compute the Casson - Donaldson invariant the author uses well known in classical algebraic geometry degeneration principle. By it, when the given Calabi - Yau manifold is deformed to a pair of quasi Fano manifolds glued upon some K3 - surface, one can compute the invariant in terms of "flag geometry" of the pairs (quasi Fano, K3 - surface). | | Source: | arXiv, math.AG/0302101 | | Services: | Forum | Review | PDF | Favorites | |
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