• 대한수학회지
• /
• 제42권6호
• /
• pp.1279-1285
• /
• 2005

Here we generalize previous work by Eisenbud-Harris and Farkas in order to prove that certain Brill-Noether divisors on the moduli space of curves have distinct supports. From this fact we deduce non-trivial regularity results for a higher co dimensional Brill-Noether locus and for the general $\frac{g+1}{2}$-gonal curve of odd genusg.

• 대한수학회지
• /
• 제44권6호
• /
• pp.1339-1350
• /
• 2007

Here we consider bihyperelliptic curves, i.e., double covers of hyperelliptic curves. By applying the theory of quadruple covers, among other things we prove that the bihyperelliptic locus in the moduli space of smooth curves is irreducible and unirational $g{\geq}4{\gamma}+2{\geq}10$.

• 대한수학회보
• /
• 제48권2호
• /
• pp.377-386
• /
• 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).

• 대한수학회지
• /
• 제47권1호
• /
• pp.41-62
• /
• 2010

In this article, we discuss a Grobner basis algorithm related to the stability of algebraic varieties in the sense of Geometric Invariant Theory. We implement the algorithm with Macaulay 2 and use it to prove the stability of certain curves that play an important role in the log minimal model program for the moduli space of curves.

• 대한수학회논문집
• /
• 제27권3호
• /
• pp.571-581
• /
• 2012

The moduli spaces of stable quasimaps unify various moduli appearing in the study of Gromov-Witten theory. This note is a survey article on the moduli of stable quasimaps, based on papers [9, 11, 18] as well as the author's talk at Kinosaki Algebraic Geometry Symposium 2010.

• 충청수학회지
• /
• 제26권3호
• /
• pp.541-545
• /
• 2013

In this paper, we explain how to get defining equations of the modular curves $X_1(2,2N)$ which show the moduli problems and present defining equations of $X_1(2,2N)$ for $N=2,3,{\ldots},8$.

• 대한수학회보
• /
• 제50권3호
• /
• pp.1029-1040
• /
• 2013

In this paper, we give sufficient conditions on a canonical genus 4 curve for it to be Chow (semi)stable.

• Korean Journal of Mathematics
• /
• 제21권3호
• /
• pp.305-309
• /
• 2013

In this paper, we give a new method to get defining equations of modular curves $X_1(2N)$ which show the moduli problems.

• 한국정밀공학회지
• /
• 제26권11호
• /
• pp.116-123
• /
• 2009

The elastic properties of core affect mechanical properties and deformation behaviours of the lightweight sandwich panel. The objective of the present paper is to estimate experimentally Young's and shear moduli of a core in internally structured boned (ISB) panel with woven metal as inner structures using the deflection theory of sandwich beam considered core stiffness. Three points bending experiments were performed to obtain force-deflection curves of the designed ISB panel in each material direction. The elastic and shear moduli of the core in each material direction were estimated from slopes and intercepts of relationships between compliance per the span length and square of the span length, respectively. The results of the estimation showed that the fabric technology of the woven metal affects the variation of the elastic properties in the core. Through the comparison of shear moduli and force-deflection curves of the proposed method and those without considering the core stiffness, it was shown that the core stiffness should be considered to estimate properly the Young's and shear moduli of ISB panels. Finally, the contribution ratio of bending and shear deflections of ISB panels to the total deflection was quantitatively examined.

• 대한수학회지
• /
• 제61권3호
• /
• pp.515-545
• /
• 2024

Consider a Noetherian domain R₀ with quotient field K₀. Let K be a finitely generated regular transcendental field extension of K₀. We construct a Noetherian domain R with Quot(R) = K that contains R₀ and embed Spec(R₀) into Spec(R). Then, we prove that key properties of abelian varieties and smooth geometrically integral projective curves over K are preserved under reduction modulo p for "almost all" p ∈ Spec(R₀).