• Bulletin of the Korean Mathematical Society
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• v.54 no.1
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• pp.265-276
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• 2017

Let K be a fan-like simplicial sphere of dimension n-1 such that its associated complete fan is strongly polytopal, and let v be a vertex of K. Let K(v) be the simplicial wedge complex obtained by applying the simplicial wedge operation to K at v, and let $v_0$ and $v_1$ denote two newly created vertices of K(v). In this paper, we show that there are infinitely many strongly polytopal fans ${\Sigma}$ over such K(v)'s, different from the canonical extensions, whose projected fans ${Proj_v}_i{\Sigma}$ (i = 0, 1) are also strongly polytopal. As a consequence, it can be also shown that there are infinitely many projective toric varieties over such K(v)'s such that toric varieties over the underlying projected complexes $K_{{Proj_v}_i{\Sigma}}$ (i = 0, 1) are also projective.

• Bulletin of the Korean Mathematical Society
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• v.60 no.6
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• pp.1705-1714
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• 2023

We explicitly construct the smooth toric Fano variety which is isomorphic to the blow-up of the projective space at torus invariant points in codimension one by anti-flips.

• Bulletin of the Korean Mathematical Society
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• v.49 no.4
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• pp.761-765
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• 2012

We prove that for a toric manifold (respectively, a quasitoric manifold) M, any graded ring isomorphism $H^*(M){\rightarrow}H^*({\Pi}_{i=1}^{m}\mathbb{C}P^{ni})$ can be realized by a diffeomorphism (respectively, a homeomorphism) ${\Pi}_{i=1}^{m}\mathbb{C}P^{ni}{\rightarrow}M$.

• Journal of the Chungcheong Mathematical Society
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• v.6 no.1
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• pp.95-104
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• 1993

There are some sufficient or necessary conditions about projectivity for toric varieties. We consider one of them and state some conditions about projectivity for a 3-dimensional compact nonsingular case which is obtained from a projective one by nonsingular equivariant blow-down.

• Journal of the Korean Mathematical Society
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• v.54 no.3
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• pp.733-748
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• 2017

We give Hodge structures on quasitoric orbifolds. We define orbifold Hodge numbers and show a correspondence of orbifold Hodge numbers for crepant resolutions of quasitoric orbifolds. In short we extend Hodge structures to a non almost complex setting.