• Title/Summary/Keyword: complete intersection

Search Result 52, Processing Time 0.025 seconds

THE GENERATORS OF COMPLETE INTERSECTION

  • Kang, Oh-Jin;Ko, Hyuong-J.
    • 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.

  • PDF

THE ARTINIAN COMPLETE INTERSECTION QUOTIENT AND THE STRONG LEFSCHETZ PROPERTY

  • Shin, Yong-Su
    • 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.

MORPHISMS BETWEEN FANO MANIFOLDS GIVEN BY COMPLETE INTERSECTIONS

  • Choe, Insong
    • 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.

  • PDF

A STRUCTURE THEOREM FOR A CLASS OF GORENSTEIN IDEALS OF GRADE FOUR

  • Cho, Yong S.
    • 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.

THE KÄHLER DIFFERENT OF A SET OF POINTS IN ℙm × ℙn

  • Hoa, Nguyen T.;Linh, Tran N.K.;Long, Le N.;Nhan, Phan T.T.;Nhi, Nguyen T.P.
    • 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 ℙm×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 ℙm×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, …, dm, 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.

A GENERALIZATION OF GIESEKER’S LEMMA

  • Kim, Sung-Ock
    • 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.

  • PDF