• Communications of the Korean Mathematical Society
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• v.17 no.2
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• pp.221-227
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• 2002

In this paper we will show that the followings ; (1) Let R be a regular local ring of dimension n. Then $A_{n-2}$(R) = 0. (2) Let R be a regular local ring of dimension n and I be an ideal in R of height 3 such that R/I is a Gorenstein ring. Then [I] = 0 in $A_{n-3}$(R). (3) Let R = V[[ $X_1$, $X_2$, …, $X_{5}$ ]]/(p+ $X_1$$^{t1}$ + $X_2$$^{t2}$ + $X_3$$^{t3}$ + $X_4$$^2$+ $X_{5}$ $^2$/), where p $\neq$2, $t_1$, $t_2$, $t_3$ are arbitrary positive integers and V is a complete discrete valuation ring with (p) = mv. Assume that R/m is algebraically closed. Then all the Chow group for R is 0 except the last Chow group.group.oup.

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

• Communications of the Korean Mathematical Society
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• v.39 no.3
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• pp.563-574
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• 2024

Given a sequence of point blow-ups of smooth n-dimensional projective varieties Z_i defined over an algebraically closed field $k,\,Z_s\,{\overset{{\pi}_s}{\longrightarrow}}\,Z_{s-1}\,{\overset{{\pi}_{s-1}}{\longrightarrow}}\,{\cdots}\,{\overset{{\pi}_2}{\longrightarrow}}\,Z_1\,{\overset{{\pi}_1}{\longrightarrow}}\,Z_0$, with Z₀ ≅ ℙⁿ, we give two presentations of the Chow ring A^•(Z_s) of its sky. The first one uses the classes of the total transforms of the exceptional components as generators and the second one uses the classes of the strict transforms ones. We prove that the skies of two sequences of point blow-ups of the same length have isomorphic Chow rings. Finally we give a characterization of the final divisors of a sequence of point blow-ups in terms of some relations defined over the Chow group of zero-cycles A₀(Z_s) of its sky.

• Communications of the Korean Mathematical Society
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• v.11 no.3
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• pp.569-573
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• 1996

We study some special cases of Chow groups of a ramified complete regular local ring R of dimension n. We prove that (a) for codimension 3 Gorenstein ideal I, [I] = 0 in $A_{n-3}(R)$ and (b) for a particular class of almost complete intersection prime ideals P of height i, [P] = 0 in $A_{n-i}(R)$.