• Title, Summary, Keyword: Picard number

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PICARD GROUP OF A SURFACE IN $P^3$

  • Kim, Sung-Ock
    • 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.

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SMOOTH HOROSPHERICAL VARIETIES OF PICARD NUMBER ONE AS LINEAR SECTIONS OF RATIONAL HOMOGENEOUS VARIETIES

  • Hong, Jaehyun
    • Journal of the Korean Mathematical Society
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    • v.53 no.2
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    • pp.433-446
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    • 2016
  • We construct projective embeddings of horospherical varieties of Picard number one by means of Fano varieties of cones over rational homogeneous varieties. Then we use them to give embeddings of smooth horospherical varieties of Picard number one as linear sections of rational homogeneous varieties.

A GENERALIZATION OF GIESEKER’S LEMMA

  • Kim, Sung-Ock
    • Bulletin of the Korean Mathematical Society
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    • v.37 no.4
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    • pp.711-719
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    • 2000
  • We generalize Gieseker\`s lemma and use it to compute Picard number of a complete intersection surface.

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SHIODA-TATE FORMULA FOR AN ABELIAN FIBERED VARIETY AND APPLICATIONS

  • Oguiso, Keiji
    • 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.

ISOMORPHISM CLASSES OF GENUS-3 POINTED TRIGONAL CURVES OVER FINITE FIELDS OF CHARACTERISTIC 2

  • Kang, Pyung-Lyun;Sun, Sun-Mi
    • Bulletin of the Korean Mathematical Society
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    • v.46 no.5
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    • pp.917-930
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    • 2009
  • We find all distinct representatives of isomorphism classes of genus-3 pointed trigonal curves and compute the number of isomorphism classes of a special class of genus-3 pointed trigonal curves including that of Picard curves over a finite field F of characteristic 2.

ON THE LINEARIZATION OF DEFECT-CORRECTION METHOD FOR THE STEADY NAVIER-STOKES EQUATIONS

  • Shang, Yueqiang;Kim, Do Wan;Jo, Tae-Chang
    • Journal of the Korean Mathematical Society
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    • v.50 no.5
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    • pp.1129-1163
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    • 2013
  • Based on finite element discretization, two linearization approaches to the defect-correction method for the steady incompressible Navier-Stokes equations are discussed and investigated. By applying $m$ times of Newton and Picard iterations to solve an artificial viscosity stabilized nonlinear Navier-Stokes problem, respectively, and then correcting the solution by solving a linear problem, two linearized defect-correction algorithms are proposed and analyzed. Error estimates with respect to the mesh size $h$, the kinematic viscosity ${\nu}$, the stability factor ${\alpha}$ and the number of nonlinear iterations $m$ for the discrete solution are derived for the linearized one-step defect-correction algorithms. Efficient stopping criteria for the nonlinear iterations are derived. The influence of the linearizations on the accuracy of the approximate solutions are also investigated. Finally, numerical experiments on a problem with known analytical solution, the lid-driven cavity flow, and the flow over a backward-facing step are performed to verify the theoretical results and demonstrate the effectiveness of the proposed defect-correction algorithms.

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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LOCI OF RATIONAL CURVES OF SMALL DEGREE ON THE MODULI SPACE OF VECTOR BUNDLES

  • Choe, In-Song
    • Bulletin of the Korean Mathematical Society
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    • v.48 no.2
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    • pp.377-386
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    • 2011
  • For a smooth algebraic curve C of genus g $\geq$ 4, let $SU_C$(r, d) be the moduli space of semistable bundles of rank r $\geq$ 2 over C with fixed determinant of degree d. When (r,d) = 1, it is known that $SU_C$(r, d) is a smooth Fano variety of Picard number 1, whose rational curves passing through a general point have degree $\geq$ r with respect to the ampl generator of Pic($SU_C$(r, d)). In this paper, we study the locus swept out by the rational curves on $SU_C$(r, d) of degree < r. As a by-product, we present another proof of Torelli theorem on $SU_C$(r, d).