Expand all Collapse all | Results 1 - 5 of 5 |
1. CMB 2011 (vol 56 pp. 306)
Real Hypersurfaces in Complex Projective Space Whose Structure Jacobi Operator is Lie $\mathbb{D}$-parallel |
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 |
2. CMB 2011 (vol 55 pp. 164)
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 |
3. CMB 2011 (vol 54 pp. 422)
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 |
4. CMB 2009 (vol 52 pp. 84)
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 |
5. CMB 2002 (vol 45 pp. 349)
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 |