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Searching for $$K3$$ fibrations. (English) Zbl 0951.81060
Summary: We present two methods for studying fibrations of Calabi-Yau manifolds embedded in toric varieties described by single weight systems. We analyze 184026 such spaces and identify among them the 124701 which are $$K3$$ fibrations. As some of the weights give rise to two or three distinct types of fibrations, the total number we find is 167406. With our methods one can also study elliptic fibrations of 3-folds and $$K3$$ surfaces. We also calculate the Hodge numbers of the 3-folds obtaining more than three times as many as were previously known.

##### MSC:
 81T30 String and superstring theories; other extended objects (e.g., branes) in quantum field theory 14J32 Calabi-Yau manifolds (algebro-geometric aspects) 32J18 Compact complex $$n$$-folds 32J81 Applications of compact analytic spaces to the sciences
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