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

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1. 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 operatorCategories:53C15, 53C40

2. 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 $2 \le j Keywords:involution, projective space bundle, indecomposable manifold, splitting principle, Stiefel-Whitney class, characteristic numberCategory:57R85 3. CMB 2011 (vol 54 pp. 422) Pérez, Juan de Dios; Suh, Young Jin  Two Conditions on the Structure Jacobi Operator for Real Hypersurfaces in Complex Projective Space We classify real hypersurfaces in complex projective space whose structure Jacobi operator satisfies two conditions at the same time. Keywords:complex projective space, real hypersurface, structure Jacobi operator, two conditionsCategories:53C15, 53B25 4. CMB 2009 (vol 52 pp. 84) Gauthier, P. M.; Zeron, E. S.  Hartogs' Theorem on Separate Holomorphicity for Projective Spaces If a mapping of several complex variables into projective space is holomorphic in each pair of variables, then it is globally holomorphic. Keywords:separately holomorphic, projective spaceCategories:32A10, 32D99, 32H99 5. CMB 2002 (vol 45 pp. 349) Coppens, Marc  Very Ample Linear Systems on Blowings-Up at General Points of Projective Spaces Let$\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 mapCategories:14E25, 14N05, 14N15
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