• Bulletin of the Korean Mathematical Society
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• v.54 no.5
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• pp.1527-1575
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• 2017

In a spirit of Givental's constructions Batyrev, Ciocan-Fontanine, Kim, and van Straten suggested Landau-Ginzburg models for smooth Fano complete intersections in Grassmannians and partial flag varieties as certain complete intersections in complex tori equipped with special functions called superpotentials. We provide a particular algorithm for constructing birational isomorphisms of these models for complete intersections in Grassmannians of planes with complex tori. In this case the superpotentials are given by Laurent polynomials. We study Givental's integrals for Landau-Ginzburg models suggested by Batyrev, Ciocan-Fontanine, Kim, and van Straten and show that they are periods for pencils of fibers of maps provided by Laurent polynomials we obtain. The algorithm we provide after minor modifications can be applied in a more general context.

• Communications of the Korean Mathematical Society
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• v.11 no.3
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• pp.627-631
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• 1996

We prove that some monomial curves are set-theoretic complete intersection of two surfaces. We also give explicity the equations of corresponding surfaces.

• Bulletin of the Korean Mathematical Society
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• v.54 no.5
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• pp.1719-1724
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• 2017

In this note, companion to the paper [10], we describe an alternative method for finding Laurent polynomials mirror-dual to complete intersections in Grassmannians of planes, in the sense discussed in [10]. This calculation follows a general method for finding torus charts on Hori-Vafa mirrors to complete intersections in toric varieties, detailed in [5] generalising the method of [8].

• Bulletin of the Korean Mathematical Society
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• v.46 no.4
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• pp.657-671
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• 2009

Buchsbaum and Eisenbud proved a structure theorem for Gorenstein ideals of grade 3. In this paper we derive a class of the perfect ideals from a class of the complete matrices. From this we give a structure theorem for complete intersections of grade g > 3.

• Bulletin of the Korean Mathematical Society
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• v.54 no.5
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• pp.1627-1654
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• 2017

We prove that in the parameter space of M-dimensional Fano complete intersections of index one and codimension two the locus of varieties that are not birationally superrigid has codimension at least ${\frac{1}{2}}(M-9)(M-10)-1$.

• Journal of the Korean Mathematical Society
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• v.34 no.3
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• pp.533-541
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• 1997

Unique factorization of 2-dimensional complete intersection is investiagted by using the determinant method introduced by D. Eisenbud.

• 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.

• Bulletin of the Korean Mathematical Society
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• v.37 no.4
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• pp.829-841
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• 2000

We classify complete intersections I of grade 3 in a regular local ring (R, M) by the number of minimal generators of a minimal prime ideal P over I. Here P is either a complete intersection or a Gorenstein ideal which is not a compete intersection.

• Journal of the Chungcheong Mathematical Society
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• v.22 no.4
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• pp.689-697
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• 2009

We study the existence of surjective morphisms between Fano manifolds of Picard number 1, when the source is given by the intersection of a cubic hypersurface and either a quadric or another cubic hypersurface in a projective space.

• Proceedings of the Korean Society of Soil and Groundwater Environment Conference
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• 2001.09a
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• pp.27-30
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• 2001

Flow and transport at fracture intersections, and their effects on network scale transport, are investigated in three-dimensional random fracture networks. Fracture intersection mixing rules complete mixing and streamline routing are defined in terms of fluxes normal to the intersection line between two fractures. By analyzing flow statistics and particle transfer probabilities distributed along fracture intersections, it is shown that for various network structures with power law size distributions of fractures, the choice of intersection mixing rule makes comparatively little difference in the overall simulated solute migration patterns. The occurrence and effects of local flows around an intersection (local flow cells) are emphasized. Transport simulations at fracture intersections indicate that local flow circulations can arise from variability within the hydraulic head distribution along intersections, and from the internal no flow condition along fracture boundaries. These local flow cells act as an effective mechanism to enhance the nondiffusive breakthrough tailing often observed in discrete fracture networks. It is shown that such non-Fickian (anomalous) solute transport can be accounted for by considering only advective transport, in the framework of a continuous time random walk model. To clarify the effect of forest environmental changes (forest type difference and clearcut) on water storage capacity in soil and stream flow, watershed had been investigated.