• Journal of the Korean Mathematical Society
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• v.39 no.5
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• pp.665-680
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• 2002

For a smooth projective irreducible algebraic curve C of odd gonality, the maximal possible dimension of the variety of special linear systems ${W^r}_d$(C) is d－3r by a result of M. Coppens et at. [4]. This bound also holds if C does not admit an involution. Furthermore it is known that if dim ${W^r}_d(C)qeq$ d-3r-1 for a curve C of odd gonality, then C is of very special type of curves by a recent progress made by G. Martens [11] and Kato-Keem [9]. The purpose of this paper is to pursue similar results for curves of even gonality which does not admit an involution.

• 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.

• Journal of the Korean Mathematical Society
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• v.42 no.2
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• pp.335-351
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• 2005

This paper concerns the relation between the degree and the projective dimension of linear systems on curves. We generalize Clifford's theorem and its improvement by Coppens and G. Martens and classify the special curves for our problem, and estimate their gonality.

• Journal of the Korean Mathematical Society
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• v.44 no.3
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• pp.565-583
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• 2007

We offer a refinement of the classical Clifford inequality about special linear series on smooth irreducible complex curves. Namely, we prove about curves of genus g and odd gonality at least 5 that for any linear series $g^r_d$ with $d{\leq}g+1$, the inequality $3r{\leq}d$ holds, except in a few sporadic cases. Further, we show that the dimension of the set of curves in the moduli space for which there exists a linear series $g^r_d$ with d<3r for $d{\leq}g+l,\;0{\leq}l{\leq}\frac{g}{2}-3$, is bounded by $2g-1+\frac{1}{3}(g+2l+1)$.

• Journal of the Korean Mathematical Society
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• v.37 no.3
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• pp.437-454
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• 2000

Let C be a smooth k-gonal curve of genus g. We study the number of pencils of degree k on C. In case $g\geqk(k-a)/2$ we state a conjecture based on a discussion on plane models for C. From previous work it is known that if C possesses a large number of pencils then C has a special plane model. From this observation the conjectures are split up in two cases : the existence of some types of plane curves should imply the existence of curves C with a given number of pencils; the non-existence of plane curves should imply the non-existence of curves C with some given large number of pencils. The non-existence part only occurs in the range $k(k-1)/2\leqg\leqk(k-1)/2] if k\geq7$. In this range we prove the existence part of the conjecture and we also prove some non-existence statements. Those result imply the conjecture in that range for $k\leq10$. The cases $k\leq6$ are handled separately.

• Journal of Environmental Science International
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• v.7 no.3
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• pp.335-348
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• 1998

The intensive meteorological observations including pibal balloon at Ungcheon, airsonde and 10m meteorological tower observations at Gulup-Do, where are located In the western coastal region, are taken to Investigate the characteristics of the upper and lower atmospheric structure and the local circulation pattern during the period of 17 to 22 September 1996. The diurnal variations of weather elements(i.e. air temperature, humidity, pressure, and Und speeds at Gulup-Do are analyzed and discussed with those at four inland meteorological stations. The vertical profiles of wind vector, ortho- gonality(Ω), and shear obtained from the pibal obsenrations are also presented to examine the change of wand structure according to the synoptic-scale pressure system's movement. The diurnal temperature changes at Gulup-Do are more sensitive than that of Inland meteorological stations In case of the mow of southwesterlies but are not dominant due to the ocean effect under the Influence of relatively cold northerlies. A well defined mixed layer Is developed from the 500m to the maximum 1700m with a significant capping Inversion layer on the top of it. It can be found from the vertical profiles of wind vector that the wind become generally strong at the interface heights between cloud lay- ers and non-cloud layers. The maximum Und shear Is appeared at the bel각t where the varlauon of wand direction Induced by the passage of synoptic-scale pressure system Is accompanied with the In- crease of Und speed. Based on the wind orthogonality, the change of wind direction with height is more complicated In cloudy day than In clear day. In case of a fair weather, the change of wand direction is showed to be at around 2km.