• Communications of the Korean Mathematical Society
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• v.11 no.4
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• pp.881-885
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• 1996

We give the optimal lower bound for the Picard number of certain surfaces in the Noether-Lefschetz locus.

• Journal of the Korean Mathematical Society
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• v.58 no.2
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• pp.351-381
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• 2021

In this paper we introduce the notion of strong Galois H-progenerator object for a finite cocommutative Hopf quasigroup H in a symmetric monoidal category C. We prove that the set of isomorphism classes of strong Galois H-progenerator objects is a subgroup of the group of strong Galois H-objects introduced in [3]. Moreover, we show that strong Galois H-progenerator objects are preserved by strong symmetric monoidal functors and, as a consequence, we obtain an exact sequence involving the associated Galois groups. Finally, to the previous functors, if H is finite, we find exact sequences of Picard groups related with invertible left H-(quasi)modules and an isomorphism Pic(HMod) ≅ Pic(C)⊕G(H∗) where Pic(HMod) is the Picard group of the category of left H-modules, Pic(C) the Picard group of C, and G(H∗) the group of group-like morphisms of the dual of H.

• Bulletin of the Korean Mathematical Society
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• v.60 no.6
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• pp.1427-1437
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• 2023

It is known that the automorphism group of a K3 surface with Picard number two is either an infinite cyclic group or an infinite dihedral group when it is infinite. In this paper, we study the generators of such automorphism groups. We use the eigenvector corresponding to the spectral radius of an automorphism of infinite order to determine the generators.

• Journal of the Korean Mathematical Society
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• v.46 no.2
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• pp.237-248
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• 2009

We give an explicit formula for the Mordell-Weil rank of an abelian fibered variety and some of its applications for an abelian fibered $hyperk{\ddot{a}}hler$ manifold. As a byproduct, we also give an explicit example of an abelian fibered variety in which the Picard number of the generic fiber in the sense of scheme is different from the Picard number of generic closed fibers.

• Journal of the Korean Mathematical Society
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• v.53 no.6
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• pp.1237-1260
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• 2016

In the paper we classify complex K3 surfaces with non-symplectic automorphism of order 16 in full generality. We show that the fixed locus contains only rational curves and points and we completely classify the seven possible configurations. If the Picard group has rank 6, there are two possibilities and if its rank is 14, there are five possibilities. In particular if the action of the automorphism is trivial on the Picard group, then we show that its rank is six.

• Economic and Environmental Geology
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• v.11 no.1
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• pp.21-37
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• 1978

The depositional environment of the Manhang and the Geumcheon Formation of the Pennsylvanian Gomog Croup is revealed to the shallow neritic marine milieu in this paper also as the results of Park (1963), Cheong(1975) and Kim (1976), through the analyses of stratigraphy, paleocurrent, properties of cross-beddings and sedimentational features. The formations contains some possible terrestrial sediments suggesting the paralic environment, which are however not recognized definitely within them. The paleocurrent analysis is made to the Manhang Formation only. The paleocurrent of the formation is known to belong to the shallow neritic longshore current. The paleocurrent analysis is based chiefly on the cross-bedding analysis, and subordinately on the texture of elastic coarse sediments. The paleocurrent mean is determined to $269^{\circ}$, that is, from east to west, of which direction is interpreted to the right angle to the slope of the basinal depository plane and also the parallel with die depositional strike, according to Klein (1960) and Selley's (1968) criteria. The variance value of paleocurrent directions of the Manhang Formation in the whole area studied is 6,374, and the values range from 3,394 to 6,957 according to the dirstricts. The paleocurreut pattern of the whole area shows polymodel, and the patterns in each district range from trimodel to quadrimodel. Those models approach to the shallow marine or paralic model of Tohill and Picard (1966), Picard and High (1968 a), Pisnak (1957) and Pettijohn (1962). The mean value of maximum inclinations of cross-beddings of the whole area is $19.9^{\circ}$ with the standard deviation of 8.4, and ranges from $15.6^{\circ}$ to $21.7^{\circ}$ in the districts. Comparing the histogram showing the frequency distribution of the maximum inclinations of cross-beddings of the Manhang Formation with the Pettijohn's (1962) histogram, it is found that the model approaches to his marine model. The Pennsylvanian Gomog Group of the coalfield is considered to have had been deposited in the pseudogeosynclinal zone on the plateau by the transgression of the Tethyan sea caused by the epirogenic movements during the Pennsylvanian Period.