• Title/Summary/Keyword: Euler Characteristic

Search Result 26, Processing Time 0.074 seconds

ON THE ORBIFOLD EULER CHARACTERISTIC OF LOG DEL PEZZO SURFACES OF RANK ONE

  • Hwang, DongSeon
    • Journal of the Korean Mathematical Society
    • /
    • v.51 no.4
    • /
    • pp.867-879
    • /
    • 2014
  • It is known that the orbifold Euler characteristic $e_{orb}(S)$ of a log del Pezzo surface S of rank one satisfies the inequality $0{\leq}e_{orb}(S){\leq}3$. In this note, we show that the orbifold Euler characteristic of S is strictly positive, i.e., 0 < $e_{orb}(S)$. Moreover, we also show, by construction, the existence of log del Pezzo surfaces of rank one with arbitrarily small orbifold Euler characteristic.

Nilpotent action by an elementary amenable group and euler characteristic

  • Lee, Jong-Bum;Park, Cnah-Young
    • Bulletin of the Korean Mathematical Society
    • /
    • v.33 no.2
    • /
    • pp.253-258
    • /
    • 1996
  • Let X be a finite connected CW-complex, $\Gamma = \pi_1(X)$ its fundamental group, $\tilde{X}$ its universal covering space. Then $\Gamma$ acts on $\tilde{X}$ by covering transformations and on the homology group $H_*(\tilde{X})$. In this note we establish the following vanishing result for the Euler characteristic $x(X)$ of X.

  • PDF

INVARIANT MEASURE AND THE EULER CHARACTERISTIC OF PROJECTIVELY ELAT MANIFOLDS

  • Jo, Kyeong-Hee;Kim, Hyuk
    • Journal of the Korean Mathematical Society
    • /
    • v.40 no.1
    • /
    • pp.109-128
    • /
    • 2003
  • In this paper, we show that the Euler characteristic of an even dimensional closed projectively flat manifold is equal to the total measure which is induced from a probability Borel measure on RP$^{n}$ invariant under the holonomy action, and then discuss its consequences and applications. As an application, we show that the Chen's conjecture is true for a closed affinely flat manifold whose holonomy group action permits an invariant probability Borel measure on RP$^{n}$ ; that is, such a closed affinly flat manifold has a vanishing Euler characteristic.

A NOTE ON BETTI NUMBERS AND RESOLUTIONS

  • Choi, Sang-Ki
    • Communications of the Korean Mathematical Society
    • /
    • v.12 no.4
    • /
    • pp.829-839
    • /
    • 1997
  • We study the Betti numbers, the Bass numbers and the resolution of modules under the change of rings. For modules of finite homological dimension, we study the Euler characteristic of them.

  • PDF

IDEAL CELL-DECOMPOSITIONS FOR A HYPERBOLIC SURFACE AND EULER CHARACTERISTIC

  • Sozen, Yasar
    • Journal of the Korean Mathematical Society
    • /
    • v.45 no.4
    • /
    • pp.965-976
    • /
    • 2008
  • In this article, we constructively prove that on a surface S with genus g$\geq$2, there exit maximal geodesic laminations with 7g-7,...,9g-9 leaves. Thus, S can have ideal cell-decompositions (i.e., S can be (ideally) triangulated by maximal geodesic laminations) with 7g-7,...,9g-9 (ideal) 1-cells. Once there is a triangulation for a compact surface, the Euler characteristic for the surface can be calculated as the alternating sum F-E+V, where F, E, and V denote the number of faces, edges, and vertices, respectively. We also prove that the same formula holds for the ideal cell decompositions.

ON THE S1-EULER CHARACTERISTIC OF THE SPACE WITH A CIRCLE ACTION ii

  • HAN, SNAG-EON
    • Honam Mathematical Journal
    • /
    • v.24 no.1
    • /
    • pp.93-101
    • /
    • 2002
  • The $S^1$-Eule characteristics of X is defined by $\bar{\chi}_{S^1}(X)\;{\in}\;HH_1(ZG)$, where G is the fundamental group of connected finite $S^1$-compact manifold or connected finite $S^1$-finite complex X and $HH_1$ is the first Hochsch ild homology group functor. The purpose of this paper is to find several cases which the $S^1$-Euler characteristic has a homotopic invariant.

  • PDF

ON A FIBER SPACE OVER A CURVE

  • Shin, Dong-Kwan
    • Communications of the Korean Mathematical Society
    • /
    • v.12 no.3
    • /
    • pp.539-541
    • /
    • 1997
  • Let X be a smooth projective threefold. Let C be a smooth projective curve and let $f : X \to C$ be a fiber space with connected fiber S. Assume that $q_1(S) = 0$. Then we have $-X(O_C)X(O_S) \leq -X(O_X)$.

  • PDF

ON A FIBER SPACE WITH CONNECTED FIBERS

  • Shin, Dong-Kwan
    • Bulletin of the Korean Mathematical Society
    • /
    • v.35 no.4
    • /
    • pp.625-627
    • /
    • 1998
  • Let f: S$\rightarrow$ C be a fiber space with connected fibers. We may have an information about a surface S from the fiber space structure. The result we have is ${\chi}({\mathcal O}_C){\chi}({\mathcal O}_F){\leq}{\chi}({\mathcal O}_S)$.

  • PDF