• Title, Summary, Keyword: complete intersections

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LAURENT PHENOMENON FOR LANDAU-GINZBURG MODELS OF COMPLETE INTERSECTIONS IN GRASSMANNIANS OF PLANES

  • Przyjalkowski, Victor;Shramov, Constantin
    • 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.

EFFICIENTLY COMPUTING TORUS CHARTS IN LANDAU-GINZBURG MODELS OF COMPLETE INTERSECTIONS IN GRASSMANNIANS OF PLANES

  • Prince, Thomas
    • 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].

SMOOTH, ISOLATED CURVES IN FAMILIES OF CALABI-YAU THREEFOLDS IN HOMOGENEOUS SPACES

  • Knutsen, Andreas Leopold
    • 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.

THE GENERATORS OF COMPLETE INTERSECTION

  • Kang, Oh-Jin;Ko, Hyuong-J.
    • 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.

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MORPHISMS BETWEEN FANO MANIFOLDS GIVEN BY COMPLETE INTERSECTIONS

  • Choe, Insong
    • 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.

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Effects of Fracture Intersection Characteristics on Transport in Three-Dimensional Fracture Networks

  • Park, Young-Jin;Lee, Kang-Kun
    • Proceedings of the Korean Society of Soil and Groundwater Environment Conference
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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.

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