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A type of the Lefschetz hyperplane section theorem on \({\mathbb{Q}\,}\) -Fano 3-folds with Picard number one and \({\frac{1}{2}(1,1,1)}\) -singularities

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Abstract

We prove a type of the Lefschetz hyperplane section theorem on \({\mathbb{Q}\,}\) -Fano 3-folds with Picard number one and \({\frac{1}{2}(1,1,1)}\) -singularities by using some degeneration method. As a byproduct, we obtain a new example of a Calabi–Yau 3-fold X with Picard number one whose invariants are

$$\left(H_X^3,\, c_2 (X) \cdot H_X, \,{{e}} (X) \right) = (8, 44, -88),$$

where H X , e(X) and c 2(X) are an ample generator of Pic(X), the topological Euler characteristic number and the second Chern class of X respectively.

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  1. Department of Mathematics Education, Hongik University, 42-1, Sangsu-Dong, Mapo-Gu, Seoul, 121-791, South Korea

    Nam-Hoon Lee

  2. School of Mathematics, Korea Institute for Advanced Study, Dongdaemun-gu, Seoul, 130-722, Korea

    Nam-Hoon Lee

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  1. Nam-Hoon Lee
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Correspondence to Nam-Hoon Lee.

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Lee, NH. A type of the Lefschetz hyperplane section theorem on \({\mathbb{Q}\,}\) -Fano 3-folds with Picard number one and \({\frac{1}{2}(1,1,1)}\) -singularities. Geom Dedicata 159, 41–49 (2012). https://doi.org/10.1007/s10711-011-9644-6

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  • DOI: https://doi.org/10.1007/s10711-011-9644-6

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