• Bulletin of the Korean Mathematical Society
• /
• v.37 no.4
• /
• pp.829-841
• /
• 2000

We classify complete intersections I of grade 3 in a regular local ring (R, M) by the number of minimal generators of a minimal prime ideal P over I. Here P is either a complete intersection or a Gorenstein ideal which is not a compete intersection.

• Journal of the Chungcheong Mathematical Society
• /
• v.32 no.2
• /
• pp.251-260
• /
• 2019

It has been little known when an Artinian (point) quotient has the strong Lefschetz property. In this paper, we find the Artinian complete intersection quotient having the SLP. More precisely, we prove that if ${\mathbb{X}}$ is a complete intersection in ${\mathbb{P}}^2$ of type (2, 2) and ${\mathbb{Y}}$ is a finite set of points in ${\mathbb{P}}^2$ such that ${\mathbb{X}}{\cup}{\mathbb{Y}}$ is a basic configuration of type (2, a) with $a{\geq}3$ or (3, a) with a = 3, 4, 5, 6, then $R/(I_{\mathbb{X}}+I_{\mathbb{Y}})$ has the SLP. We also show that if ${\mathbb{X}}$ is a complete intersection in ${\mathbb{P}}^2$ of type (3, 2) and ${\mathbb{Y}}$ is a finite set of points in ${\mathbb{P}}^2$ such that ${\mathbb{X}}{\cup}{\mathbb{Y}}$ is a basic configuration of type (3, 3) or (3, 4), then $R/(I_{\mathbb{X}}+I_{\mathbb{Y}})$ has the SLP.

• Journal of the Korean Mathematical Society
• /
• v.34 no.3
• /
• pp.533-541
• /
• 1997

Unique factorization of 2-dimensional complete intersection is investiagted by using the determinant method introduced by D. Eisenbud.

• The Pure and Applied Mathematics
• /
• v.29 no.2
• /
• pp.201-206
• /
• 2022

Let X be a nodal complete intersection 3-fold defined by a hypersurface in ℙ⁵ of degree n and a smooth quadratic hypersurface in ℙ⁵ . Then we show that X is factorial if it has at most n² - n + 1 nodes and contains no 2-planes, where n = 3, 4.

• Journal of the Chungcheong Mathematical Society
• /
• v.22 no.4
• /
• pp.689-697
• /
• 2009

We study the existence of surjective morphisms between Fano manifolds of Picard number 1, when the source is given by the intersection of a cubic hypersurface and either a quadric or another cubic hypersurface in a projective space.

• Communications of the Korean Mathematical Society
• /
• v.11 no.3
• /
• pp.627-631
• /
• 1996

We prove that some monomial curves are set-theoretic complete intersection of two surfaces. We also give explicity the equations of corresponding surfaces.

• Honam Mathematical Journal
• /
• v.36 no.3
• /
• pp.605-622
• /
• 2014

We provide a minimal free resolution for a class of Gorenstein ideal of grade 4 which is the sum of an almost complete intersection J of grade 3 and a perfect ideal I of grade 3 with type 2 and ${\lambda}(I)$ > 0 geometrically linked by a regular sequence, where I is generated by odd elements.

• Honam Mathematical Journal
• /
• v.36 no.2
• /
• pp.387-398
• /
• 2014

In this paper, we give a structure theorem for a class of Gorenstein ideal of grade 4 which is the sum of an almost complete intersection of grade 3 and a Gorenstein ideal of grade 3 geometrically linked by a regular sequence. We also present the Hilbert function of a Gorenstein ideal of grade 4 induced by a Gorenstein matrix f.

• Bulletin of the Korean Mathematical Society
• /
• v.59 no.4
• /
• pp.929-949
• /
• 2022

Given an ACM set 𝕏 of points in a multiprojective space ℙ^m×ℙⁿ over a field of characteristic zero, we are interested in studying the Kähler different and the Cayley-Bacharach property for 𝕏. In ℙ¹×ℙ¹, the Cayley-Bacharach property agrees with the complete intersection property and it is characterized by using the Kähler different. However, this result fails to hold in ℙ^m×ℙⁿ for n > 1 or m > 1. In this paper we start an investigation of the Kähler different and its Hilbert function and then prove that 𝕏 is a complete intersection of type (d₁, …, d_m, d'₁, …, d'_n) if and only if it has the Cayley-Bacharach property and the Kähler different is non-zero at a certain degree. We characterize the Cayley-Bacharach property of 𝕏 under certain assumptions.

• Bulletin of the Korean Mathematical Society
• /
• v.37 no.4
• /
• pp.711-719
• /
• 2000

We generalize Gieseker\`s lemma and use it to compute Picard number of a complete intersection surface.