• Title/Summary/Keyword: projective dimension

Search Result 52, Processing Time 0.023 seconds

ON SOME CR-SUBMANIFOLDS OF (n-1) CR-DIMENSION IN A COMPLEX PROJECTIVE SAPCE

  • Kwon, Jung-Hwan
    • Communications of the Korean Mathematical Society
    • /
    • v.13 no.1
    • /
    • pp.85-94
    • /
    • 1998
  • The purpose of this paper is to give sample characterizations of n-dimensional CR-submanifolds of (n-1) CR-semifolds of (n-1) CR-dimension immersed in a complex projective space $CP^{(n+p)/2}$ with Fubini-Study metric and we study an n-dimensional compact, orientable, minimal CR-submanifold of (n-1) CR-dimension in $CP^{(n+p)/2}$.

  • PDF

QR-SUBMANIFOLDS OF MAXIMAL QR-DIMENSION IN QUATERNIONIC PROJECTIVE SPACE

  • Kim, Hyang-Sook;Pak, Jin-Suk
    • Journal of the Korean Mathematical Society
    • /
    • v.42 no.4
    • /
    • pp.655-672
    • /
    • 2005
  • The purpose of this paper is to study n-dimensional QR-submanifolds of maximal QR-dimension isometrically immersed in a quaternionic projective space and to give sufficient conditions in order for such a submanifold to be a tube over a quaternionic invariant submanifold.

DEPTH OF TOR

  • Choi, Sang-Ki
    • Bulletin of the Korean Mathematical Society
    • /
    • v.37 no.1
    • /
    • pp.103-108
    • /
    • 2000
  • Using spectral sequences we calculate the highest nonvanishing index of Tor for modules of finite projective dimension. The result is applied to compute the depth of the highest nonvanishing Tor. This is one of the cases when a problem of Auslander is positive.

  • PDF

A CHARACTERIZATION OF PROJECTIVE GEOMETRIES

  • Yoon, Young-Jin
    • Bulletin of the Korean Mathematical Society
    • /
    • v.32 no.2
    • /
    • pp.215-219
    • /
    • 1995
  • The most fundamental examples of (combinatorial) geometries are projective geometries PG(n - 1,q) of dimension n - 1, representable over GF(q), where q is a prime power. Every upper interval of a projective geometry is a projective geometry. The Whitney numbers of the second kind are Gaussian coefficients. Every flat of a projective geometry is modular, so the projective geometry is supersolvable in the sense of Stanley [6].

  • PDF

REAL n-DIMENSIONAL QR-SUBMANIFOLDS OF MAXIMAL QR-DIMENSION IMMERSED IN QP(n+p)/4

  • Kim, Hyang-Sook;Kwon, Jung-Hwan;Pak, Jin-Suk
    • Communications of the Korean Mathematical Society
    • /
    • v.24 no.1
    • /
    • pp.111-125
    • /
    • 2009
  • The purpose of this paper is to study n-dimensional QR-submanifolds of (p-1) QR-dimension immersed in a quaternionic projective space $QP^{(n+p)/4}$ of constant Q-sectional curvature 4 and especially to determine such submanifolds under the additional condition concerning with shape operator.

INTEGRAL CHOW MOTIVES OF THREEFOLDS WITH K-MOTIVES OF UNIT TYPE

  • Gorchinskiy, Sergey
    • Bulletin of the Korean Mathematical Society
    • /
    • v.54 no.5
    • /
    • pp.1827-1849
    • /
    • 2017
  • We prove that if a smooth projective algebraic variety of dimension less or equal to three has a unit type integral K-motive, then its integral Chow motive is of Lefschetz type. As a consequence, the integral Chow motive is of Lefschetz type for a smooth projective variety of dimension less or equal to three that admits a full exceptional collection.

ON THE PROJECTIVE FOURFOLDS WITH ALMOST NUMERICALLY POSITIVE CANONICAL DIVISORS

  • Fukuda, Shigetaka
    • Bulletin of the Korean Mathematical Society
    • /
    • v.43 no.4
    • /
    • pp.763-770
    • /
    • 2006
  • Let X be a four-dimensional projective variety defined over the field of complex numbers with only terminal singularities. We prove that if the intersection number of the canonical divisor K with every very general curve is positive (K is almost numerically positive) then every very general proper subvariety of X is of general type in ';he viewpoint of geometric Kodaira dimension. We note that the converse does not hold for simple abelian varieties.

ON THE FINITENESS OF REAL STRUCTURES OF PROJECTIVE MANIFOLDS

  • Kim, Jin Hong
    • Bulletin of the Korean Mathematical Society
    • /
    • v.57 no.1
    • /
    • pp.109-115
    • /
    • 2020
  • Recently, Lesieutre constructed a 6-dimensional projective variety X over any field of characteristic zero whose automorphism group Aut(X) is discrete but not finitely generated. As an application, he also showed that X is an example of a projective variety with infinitely many non-isomorphic real structures. On the other hand, there are also several finiteness results of real structures of projective varieties. The aim of this short paper is to give a sufficient condition for the finiteness of real structures on a projective manifold in terms of the structure of the automorphism group. To be more precise, in this paper we show that, when X is a projective manifold of any dimension≥ 2, if Aut(X) does not contain a subgroup isomorphic to the non-abelian free group ℤ ∗ ℤ, then there are only finitely many real structures on X, up to ℝ-isomorphisms.

GORENSTEIN QUASI-RESOLVING SUBCATEGORIES

  • Cao, Weiqing;Wei, Jiaqun
    • Journal of the Korean Mathematical Society
    • /
    • v.59 no.4
    • /
    • pp.733-756
    • /
    • 2022
  • In this paper, we introduce the notion of Gorenstein quasiresolving subcategories (denoted by 𝒢𝒬𝓡𝒳 (𝓐)) in term of quasi-resolving subcategory 𝒳. We define a resolution dimension relative to the Gorenstein quasi-resolving categories 𝒢𝒬𝓡𝒳 (𝓐). In addition, we study the stability of 𝒢𝒬𝓡𝒳 (𝓐) and apply the obtained properties to special subcategories and in particular to modules categories. Finally, we use the restricted flat dimension of right B-module M to characterize the finitistic dimension of the endomorphism algebra B of a 𝒢𝒬𝒳-projective A-module M.