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Local mirror symmetry: Calculations and interpretations. (English) Zbl 0976.32012
Summary: We describe local mirror symmetry from a mathematical point of view and make several A-model calculations using the mirror principle (localization). Our results agree with B-model computations from solutions of Picard-Fuchs differential equations constructed from the local geometry near a Fano surface within a Calabi-Yau manifold. We interpret the Gromov-Witten-type numbers from an enumerative point of view. We also describe the geometry of singular surfaces and show how the local invariants of singular surfaces agree with the smooth cases when they occur as complete intersections.

MSC:
32J99 Compact analytic spaces
14J99 Surfaces and higher-dimensional varieties
81T30 String and superstring theories; other extended objects (e.g., branes) in quantum field theory
32Q25 Calabi-Yau theory (complex-analytic aspects)
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