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Search: All articles in the CMB digital archive with keyword characteristic

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1. CMB 2014 (vol 57 pp. 658)

Thang, Nguyen Tat
 Admissibility of Local Systems for some Classes of Line Arrangements Let $\mathcal{A}$ be a line arrangement in the complex projective plane $\mathbb{P}^2$ and let $M$ be its complement. A rank one local system $\mathcal{L}$ on $M$ is admissible if roughly speaking the cohomology groups $H^m(M,\mathcal{L})$ can be computed directly from the cohomology algebra $H^{*}(M,\mathbb{C})$. In this work, we give a sufficient condition for the admissibility of all rank one local systems on $M$. As a result, we obtain some properties of the characteristic variety $\mathcal{V}_1(M)$ and the Resonance variety $\mathcal{R}_1(M)$. Keywords:admissible local system, line arrangement, characteristic variety, multinet, resonance varietyCategories:14F99, 32S22, 52C35, 05A18, 05C40, 14H50

2. CMB 2011 (vol 55 pp. 368)

Nie, Zhaohu
 The Secondary Chern-Euler Class for a General Submanifold We define and study the secondary Chern-Euler class for a general submanifold of a Riemannian manifold. Using this class, we define and study the index for a vector field with non-isolated singularities on a submanifold. As an application, we give conceptual proofs of a result of Chern. Keywords:secondary Chern-Euler class, normal sphere bundle, Euler characteristic, index, non-isolated singularities, blow-upCategory:57R20

3. CMB 2011 (vol 55 pp. 164)

Pergher, Pedro L. Q.
 Involutions Fixing $F^n \cup \{\text{Indecomposable}\}$ Let $M^m$ be an $m$-dimensional, closed and smooth manifold, equipped with a smooth involution $T\colon M^m \to M^m$ whose fixed point set has the form $F^n \cup F^j$, where $F^n$ and $F^j$ are submanifolds with dimensions $n$ and $j$, $F^j$ is indecomposable and $n >j$. Write $n-j=2^pq$, where $q \ge 1$ is odd and $p \geq 0$, and set $m(n-j) = 2n+p-q+1$ if $p \leq q + 1$ and $m(n-j)= 2n + 2^{p-q}$ if $p \geq q$. In this paper we show that $m \le m(n-j) + 2j+1$. Further, we show that this bound is \emph{almost} best possible, by exhibiting examples $(M^{m(n-j) +2j},T)$ where the fixed point set of $T$ has the form $F^n \cup F^j$ described above, for every $2 \le j Keywords:involution, projective space bundle, indecomposable manifold, splitting principle, Stiefel-Whitney class, characteristic numberCategory:57R85 4. CMB 2010 (vol 54 pp. 56) Dinh, Thi Anh Thu  Characteristic Varieties for a Class of Line Arrangements Let$\mathcal{A}$be a line arrangement in the complex projective plane$\mathbb{P}^2$, having the points of multiplicity$\geq 3$situated on two lines in$\mathcal{A}$, say$H_0$and$H_{\infty}$. Then we show that the non-local irreducible components of the first resonance variety$\mathcal{R}_1(\mathcal{A})$are 2-dimensional and correspond to parallelograms$\mathcal{P}$in$\mathbb{C}^2=\mathbb{P}^2 \setminus H_{\infty}$whose sides are in$\mathcal{A}$and for which$H_0$is a diagonal. Keywords:local system, line arrangement, characteristic variety, resonance varietyCategories:14C21, 14F99, 32S22, 14E05, 14H50 5. CMB 2004 (vol 47 pp. 22) Goto, Yasuhiro  A Note on the Height of the Formal Brauer Group of a$K3$Surface Using weighted Delsarte surfaces, we give examples of$K3$surfaces in positive characteristic whose formal Brauer groups have height equal to$5$,$8$or$9$. These are among the four values of the height left open in the article of Yui \cite{Y}. Keywords:formal Brauer groups,$K3\$ surfaces in positive, characteristic, weighted Delsarte surfacesCategories:14L05, 14J28
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