• Journal of the Chungcheong Mathematical Society
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• v.30 no.3
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• pp.331-335
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• 2017

We construct Calabi-Yau threefolds by smoothing normal crossing varieties, which are made from the building blocks of $G_2-manifolds$. We compute the Hodge numbers of those Calabi-Yau threefolds. Some of those Hodge number pairs ($h^{1,1}$, $h^{1,2}$) do not overlap with those of Calabi-Yau threefolds constructed in the toric setting.

• Kyungpook Mathematical Journal
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• v.57 no.2
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• pp.327-329
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• 2017

For any even integer n, we show that there exists a log Calabi-Yau threefold (Y, D) such that the Euler characteristic of Y is n. Furthermore Y is smooth and D is smooth anticanonical section of Y that is a K3 surface.

• Journal of the Korean Mathematical Society
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• v.50 no.5
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• pp.1033-1050
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• 2013

We show the existence of smooth isolated curves of different degrees and genera in Calabi-Yau threefolds that are complete intersections in homogeneous spaces. Along the way, we classify all degrees and genera of smooth curves on BN general K3 surfaces of genus ${\mu}$, where $5{\leq}{\mu}{\leq}10$. By results of Mukai, these are the K3 surfaces that can be realised as complete intersections in certain homogeneous spaces.

• Kyungpook Mathematical Journal
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• v.53 no.2
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• pp.149-174
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• 2013

In a previous paper, we described some Siegel modular threefolds which admit a Calabi-Yau model. Using a different method we give in this paper an enlarged list of such varieties. Basic for this method is a paper of van Geemen and Nygaard. They study a variety $\mathcal{X}$ that is the complete intersection of four quadrics in $\mathbb{P}^7(\mathbb{C})$. This is biholomorphic equivalent to the Satake compactification of $\mathcal{H}_2/{\Gamma}^{\prime}$ for a certain subgroup ${\Gamma}^{\prime}{\subset}Sp(2,\mathbb{Z})$ and it will be the starting point of our investigation. It has been pointed out that a (projective) small resolution of this variety is a rigid Calabi-Yau manifold $\tilde{\mathcal{X}}$. Then we will consider the action of quotients of modular groups on $\mathcal{X}$ and study possible resolutions that admits a Calabi-Yau model in the category of complex spaces.