• Communications of the Korean Mathematical Society
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• v.35 no.1
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• pp.43-61
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• 2020

We extend the work of A. Beauville on rank 2 vector bundles on a smooth curve in several directions. We give families of examples with large dimension, add new existence and non-existence results and prove the existence of indecomposable limits with arbitrary rank. To construct the large dimensional families we use the examples of limits of rank 2 trivial bundles on ℙ² and ℙ³ due to C. Banica. We also consider a more flexible notion: limits of trivial bundles on nearby curves.

• Kyungpook Mathematical Journal
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• v.45 no.2
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• pp.167-169
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• 2005

Here we introduce and study vector bundles, E, on a smooth projective curve X having many "spread" sections and for which $E^{*}\;{\otimes}{\omega}X$ has many "spread" sections. We show that no such bundle exists on X if the gonality of X is too low.

• 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).

• Journal of applied mathematics & informatics
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• v.40 no.3_4
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• pp.587-601
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• 2022

We find the characterizations of the curvatures of Legendre curves and magnetic curves in Kenmotsu manifolds with C-parallel and C-proper mean curvature vector fields in the tangent and normal bundles. Finally, an illustrative example is presented.

• Journal of the Korean Mathematical Society
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• v.46 no.3
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• pp.589-607
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• 2009

In this paper we study arithmetically Cohen-Macaulay (ACM for short) vector bundles $\varepsilon$ of rank k $\geq$ 3 on hypersurfaces $X_r\;{\subset}\;{\mathbb{P}}^4$ of degree r $\geq$ 1. We consider here mainly the case of degree r = 4, which is the first unknown case in literature. Under some natural conditions for the bundle $\varepsilon$ we derive a list of possible Chern classes ($c_1$, $c_2$, $c_3$) which may arise in the cases of rank k = 3 and k = 4, when r = 4 and we give several examples.