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NOETHERIAN RINGS OF KRULL DIMENSION 2
신용수 한국전산응용수학회 2010 Journal of applied mathematics & informatics Vol.28 No.3
We prove that a maximal ideal M of D[x] has two generators and is of the form <p, q(x)>where p is an irreducible element in a PID D having infinitely many nonassociate irreducible elements and q(x) is an irreducible non-constant polynomial in D[x]. Moreover, we find how minimal generators of maximal ideals of a polynomial ring D[x] over a DVR D consist of and how many generators those maximal ideals have.
Secant varieties to the variety of reducible forms
신용수 충청수학회 2014 충청수학회지 Vol.27 No.1
We completely classify the dimension of secant varieties Sec1(X λ2)to the variety of reducible forms in|[x0,x1,x2]when λ =(1,...,1,3,....,3), and also show that they are all non-defective.
A point star-configuration in $\P^n$ having generic Hilbert function
신용수 충청수학회 2015 충청수학회지 Vol.28 No.1
We ¯nd a necessary and su±cient condition for whicha point star-con¯guration in Pn has generic Hilbert function. Moreprecisely, a point star-con¯guration in Pn de¯ned by general formsof degrees d1; : : : ; ds with 3 · n · s has generic Hilbert functionif and only if d1 = ¢ ¢ ¢ = ds¡1 = 1 and ds = 1; 2. Otherwise,the Hilbert function of a point star-con¯guration in Pn is NEVERgeneric.
Some applications of the union of star-configurations in P^n
신용수 충청수학회 2011 충청수학회지 Vol.24 No.4
It has been proved that if X^((s,s)) is the union of two linear star-configurations in P^2 of type s × s, then (I_(X^((s,s))))_s ≠ {0} for s=3,4,5, and (I_(X^((s,s))))_s={0} for s ≥ 6. We extend P^2 to P^n and show that if X^((s,s)) is the union of two linear star-configurations in P^n, then (I_(X^((s,s))))_s={0} for n ≥ 3 and s ≥ 3. Using this generalization, we also prove that the secant variety Sec_1(Split_s(P^n)) has the expected dimension 2ns+1 for n ≥ 3 and s ≥ 3.
On The Hilbert Function of The Union of Two Linear Star-Configurations in P2
신용수 충청수학회 2012 충청수학회지 Vol.25 No.3
t has been proved that the union of two linear star-configura- tions in $\P^2$ of type $t\times s$ for $3\le t \le 9$ and $3\le t\le s$ has generic Hilbert function. We extend the condition to $ t=10$, so that it is true for $3\le t \le 10$, which generalizes the result of \cite{S:1}.