• Journal of applied mathematics & informatics
• /
• v.3 no.1
• /
• pp.65-78
• /
• 1996

The properties of a toric variety have strong connection with the combinatorial structure of the corresponding fan and the rela-tions among the generators. Using this fact we have described explic-itly the Chow ring for a Q-factorial toric variety as the Stanley-Reisner ring for the corresponding fan modulo the linear equivalence relation. In this paper we calculate the Chow ring for 3-dimensional Q-factorial toric varieties having one bad isolated singularity.

• Journal of the Korean Mathematical Society
• /
• v.46 no.1
• /
• pp.125-150
• /
• 2009

We analytically construct the versal deformation space of resolution of normal isolated singularities based on the formalism in [9].

• Journal of the Korean Mathematical Society
• /
• v.37 no.2
• /
• pp.193-223
• /
• 2000

In the late 1970's, M. Kuranishi proposed to control the moduli of the germ of a normal Stein space by deformations of the CR structure on the boundary. I this paper, we will see that it is naturally accomplished by considering stably embeddable deformations of CR structures.

• Journal of the Korean Mathematical Society
• /
• v.40 no.4
• /
• pp.709-725
• /
• 2003

We give an analytic approach to the versal deformation of a resolution of a germ of normal isolated singularities. In this paper, we treat only formal deformation theory and it is applied to complete the CR-description of the simultaneous resolution of a cone eve. a rational curve of degree n in P$^{n}$ (n $\leq$ 4).

• Journal of the Korean Society for Industrial and Applied Mathematics
• /
• v.6 no.1
• /
• pp.59-65
• /
• 2002

In this paper, we consider some homogeneous maps from a cone over 2-spheres and determines whether they become energy minimizing maps or not. In fact, any homogeneous map from a standard cone over 2-sphere of radius smaller than 1 can not be a minimizing harmonic map.

• Bulletin of the Korean Mathematical Society
• /
• v.52 no.4
• /
• pp.1213-1223
• /
• 2015

We examine a family of isolated complex surface singularities whose exceptional curves consist of two complex curves with high genera intersecting transversally. Topological data of smoothings of these singularities are determined. We use these computations to construct symplectic 4-manifolds by replacing neighborhoods of the exceptional curves with smoothings of the singularities.

• Bulletin of the Korean Mathematical Society
• /
• v.26 no.2
• /
• pp.169-173
• /
• 1989

Let V={(x,y,z):f=z$^{n}$ -npz+(n-1)q=0 for n .geq. 3} be a compled analytic subvariety of a polydisc in $C^{3}$ where p=p(x,y) and q=q(x,y) are holomorphic near (x,y)=(0,0) and f is an irreducible Weierstrass polynomial in z of multiplicity n. Suppose that V has an isolated singular point at the origin. Recall that the z-discriminant of f is D(f)=c(p$^{n}$ -q$^{n-1}$) for some number c. Suppose that D(f) is square-free. then we prove that by Theorem 2.1 .mu.(p$^{n}$ -q$^{n-1}$)=.mu.(f)-(n-1)+n(n-2)I(p,q)+1 where .mu.(f), .mu. p$^{n}$ -q$^{n-1}$are the corresponding Milnor numbers of f, p$^{n}$ -q$^{n-1}$, respectively and I(p,q) is the intersection number of p and q at the origin. By one of applications suppose that W$_{t}$ ={(x,y,z):g$_{t}$ =z$^{n}$ -np$_{t}$ $^{n-1}$z+(n-1)q$_{t}$ $^{n-1}$=0} is a smooth family of complex analytic varieties near t=0 each of which has an isolated singularity at the origin, satisfying that the z-discriminant of g$_{t}$ , that is, D(g$_{t}$ ) is square-free. If .mu.(g$_{t}$ ) are constant near t=0, then we prove that the family of plane curves, D(g$_{t}$ ) are equisingular and also D(f$_{t}$ ) are equisingular near t=0 where f$_{t}$ =z$^{n}$ -np$_{t}$ z+(n-1)q$_{t}$ =0.}$ =0.

• ALGAE
• /
• v.37 no.1
• /
• pp.1-14
• /
• 2022

Cyanobacteria are distributed worldwide, and many new cyanobacterial species are discovered in tropical region. The Nostoc-like genus Amazonocrinis has been separated from the genus Nostoc based on polyphasic methods. However, species diversity within this genus remains poorly understood systematically because only one species (Amazonocrinis nigriterrae) has been described. In this study, two novel strains (NUACC02 and NUACC03) were isolated from moist rice field soil in Thailand. These two strains were characterized using a polyphasic approach, based on morphology, 16S rRNA phylogenetic analysis, internal transcribed spacer secondary structure and ecology. Phylogenetic analyses based on 16S rRNA gene sequences confirmed that the two novel strains formed a monophyletic clade related to the genus Amazonocrinis and were distant from the type species A. nigriterrae. The 16S rRNA gene sequence similarity (<98.1%) between novel strains and all other closely related taxa including the Amazonocrinis members exceeded the cutoff for species delimitation in bacteriology, reinforcing the presence of a new Amazonocrinis species. Furthermore, the novel strains possessed unique phenotypic characteristics such as the presence of the sheath, necridia-like cells, larger cell dimension and akinete cell arrangement in long-chains and the singularity of D1-D1', Box-B, V2, and V3 secondary structures that distinguished them from other Amazonocrinis members. Considering all the results, we described our two strains as Amazonocrinis thailandica sp. nov. in accordance with the International Code of Nomenclature for Algae, Fungi and Plants.