• 제목/요약/키워드: Euler Characteristic

검색결과 26건 처리시간 0.036초

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

  • Hwang, DongSeon
    • 대한수학회지
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    • 제51권4호
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    • pp.867-879
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    • 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
    • 대한수학회보
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    • 제33권2호
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    • pp.253-258
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    • 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.

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INVARIANT MEASURE AND THE EULER CHARACTERISTIC OF PROJECTIVELY ELAT MANIFOLDS

  • Jo, Kyeong-Hee;Kim, Hyuk
    • 대한수학회지
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    • 제40권1호
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    • pp.109-128
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    • 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
    • 대한수학회논문집
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    • 제12권4호
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    • pp.829-839
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    • 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.

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IDEAL CELL-DECOMPOSITIONS FOR A HYPERBOLIC SURFACE AND EULER CHARACTERISTIC

  • Sozen, Yasar
    • 대한수학회지
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    • 제45권4호
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    • pp.965-976
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    • 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
    • 호남수학학술지
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    • 제24권1호
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    • pp.93-101
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    • 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.

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ON A FIBER SPACE OVER A CURVE

  • Shin, Dong-Kwan
    • 대한수학회논문집
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    • 제12권3호
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    • pp.539-541
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    • 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 $-X(O_C)X(O_S) \leq -X(O_X)$.

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AFFINE MANIFOLD WITH MEASURE PRESERVING PROJECTIVE HOLONOMY GROUP

  • Park, Yeong-Su
    • 대한수학회보
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    • 제38권1호
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    • pp.157-161
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    • 2001
  • In this paper, we prove that an affine manifold M is finitely covered by a manifold $\overline{M}$ where $\overline{M}$ is radiant or the tangent bundle of $\overline{M}$ has a conformally flat vector subbundle of the projective holonomy group of M admits an invariant probability Borel measure. This implies that$x^M$is zero.

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ON A FIBER SPACE WITH CONNECTED FIBERS

  • Shin, Dong-Kwan
    • 대한수학회보
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    • 제35권4호
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    • pp.625-627
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    • 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 ${\chi}({\mathcal O}_C){\chi}({\mathcal O}_F){\leq}{\chi}({\mathcal O}_S)$.

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