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

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1. CMB 2013 (vol 57 pp. 72)

Grari, A.
Un Anneau Commutatif associé à un design symétrique
Dans les articles \cite{1}, \cite{2} et \cite{3}; l'auteur développe une représentation d'un plan projectif fini par un anneau commutatif unitaire dont les propriétés algébriques dépendent de la structure géométrique du plan. Dans l'article \cite{4}; il étend cette représentation aux designs symétriques. Cependant l'auteur de l'article \cite{7} fait remarquer que la multiplication définie dans ce cas ne peut être associative que si le design est un plan projectif. Dans ce papier on mènera une étude de cette représentation dans le cas des designs symétriques. On y montrera comment on peut faire associer un anneau commutatif unitaire à tout design symétrique , on y précisera certaines de ses propriétés, en particulier, celles qui relèvent de son invariance. On caractérisera aussi les géométries projectives finies de dimension supérieure moyennant cette représentation.

Keywords:projective planes, symmetric designs, commutative rings
Categories:05B05, 16S99

2. CMB 2011 (vol 56 pp. 306)

Pérez, Juan de Dios; Suh, Young Jin
Real Hypersurfaces in Complex Projective Space Whose Structure Jacobi Operator is Lie $\mathbb{D}$-parallel
We prove the non-existence of real hypersurfaces in complex projective space whose structure Jacobi operator is Lie $\mathbb{D}$-parallel and satisfies a further condition.

Keywords:complex projective space, real hypersurface, structure Jacobi operator
Categories:53C15, 53C40

3. CMB 2011 (vol 56 pp. 203)

Tall, Franklin D.
Productively Lindelöf Spaces May All Be $D$
We give easy proofs that (a) the Continuum Hypothesis implies that if the product of $X$ with every Lindelöf space is Lindelöf, then $X$ is a $D$-space, and (b) Borel's Conjecture implies every Rothberger space is Hurewicz.

Keywords:productively Lindelöf, $D$-space, projectively $\sigma$-compact, Menger, Hurewicz
Categories:54D20, 54B10, 54D55, 54A20, 03F50

4. CMB 2011 (vol 55 pp. 138)

Li, Benling; Shen, Zhongmin
Projectively Flat Fourth Root Finsler Metrics
In this paper, we study locally projectively flat fourth root Finsler metrics and their generalized metrics. We prove that if they are irreducible, then they must be locally Minkowskian.

Keywords:projectively flat, Finsler metric, fourth root Finsler metric
Category:53B40

5. 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 number
Category:57R85

6. CMB 2011 (vol 54 pp. 422)

Pérez, Juan de Dios; Suh, Young Jin
Two Conditions on the Structure Jacobi Operator for Real Hypersurfaces in Complex Projective Space
We classify real hypersurfaces in complex projective space whose structure Jacobi operator satisfies two conditions at the same time.

Keywords:complex projective space, real hypersurface, structure Jacobi operator, two conditions
Categories:53C15, 53B25

7. CMB 2009 (vol 52 pp. 84)

Gauthier, P. M.; Zeron, E. S.
Hartogs' Theorem on Separate Holomorphicity for Projective Spaces
If a mapping of several complex variables into projective space is holomorphic in each pair of variables, then it is globally holomorphic.

Keywords:separately holomorphic, projective space
Categories:32A10, 32D99, 32H99

8. CMB 2002 (vol 45 pp. 349)

Coppens, Marc
Very Ample Linear Systems on Blowings-Up at General Points of Projective Spaces
Let $\mathbf{P}^n$ be the $n$-dimensional projective space over some algebraically closed field $k$ of characteristic $0$. For an integer $t\geq 3$ consider the invertible sheaf $O(t)$ on $\mathbf{P}^n$ (Serre twist of the structure sheaf). Let $N = \binom{t+n}{n}$, the dimension of the space of global sections of $O(t)$, and let $k$ be an integer satisfying $0\leq k\leq N - (2n+2)$. Let $P_1,\dots,P_k$ be general points on $\mathbf{P}^n$ and let $\pi \colon X \to \mathbf{P}^n$ be the blowing-up of $\mathbf{P}^n$ at those points. Let $E_i = \pi^{-1} (P_i)$ with $1\leq i\leq k$ be the exceptional divisor. Then $M = \pi^* \bigl( O(t) \bigr) \otimes O_X (-E_1 - \cdots -E_k)$ is a very ample invertible sheaf on $X$.

Keywords:blowing-up, projective space, very ample linear system, embeddings, Veronese map
Categories:14E25, 14N05, 14N15

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