共查询到20条相似文献,搜索用时 0 毫秒
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Michael Fraboni 《Mathematische Zeitschrift》2006,254(3):553-566
Let C be a nowhere dense compact analytic subset of a 2-dimensional complex manifold X. A result of Napier is the construction of a neighborhood V of C such that for any covering space
in which
is holomorphically convex, there is a C
∞ exhaustion function φ on
which is strictly plurisubharmonic on π-1(V) away from the compact irreducible components of
. Colţoiu and Vajaitu obtained a q-convex version of this result for C a q-dimensional fiber of a proper surjective submersion X→Y. The goal of this paper is a similar version for Cprojective. 相似文献
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Jörg Winkelmann 《manuscripta mathematica》2000,102(2):159-161
We show that for a quotient of a complex Lie group by a lattice there does not exist any open equivariant holomorphic embedding
into a larger complex space.
Received: 17 June 1999 相似文献
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We show that ifM is the total space of a holomorphic bundle with base space a simply connected homogeneous projective variety and fibre and
structure group a compact complex torus, then the identity component of the automorphism group ofM acts trivially on the Dolbeault cohomology ofM. We consider a class of compact complex homogeneous spacesW, which we call generalized Hopf manifolds, which are diffeomorphic to S1 ×K/L whereK is a compact connected simple Lie group andL is the semisimple part of the centralizer of a one dimensional torus inK. We compute the Dolbeault cohomology ofW. We compute the Picard group of any generalized Hopf manifold and show that every line bundle over a generalized Hopf manifold
arises from a representation of its fundamental group. 相似文献
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Using the concept of inner integral curves defined by Hirschowitz we generalize a recent result by Kim, Levenberg and Yamaguchi concerning the obstruction of a pseudoconvex domain spread over a complex homogeneous manifold to be Stein. This is then applied to study the holomorphic reduction of pseudoconvex complex homogeneous manifolds X = G/H. Under the assumption that G is solvable or reductive we prove that X is the total space of a G-equivariant holomorphic fiber bundle over a Stein manifold such that all holomorphic functions on the fiber are constant. 相似文献
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Zalman Rubinstein 《Journal of Mathematical Analysis and Applications》1980,74(2):464-474
Two basic analytic functions α(z) and β(z) defined in domains depending on the location of the zeros of a complex polynomial P(z) are given by and P = (z ? β)n. These functions are studied with respect to their growth and their Laurent expansion coefficients. Applications to the location of zeros of complex polynomials are indicated. 相似文献
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Let X be a compact complex homogeneous manifold and let Aut(X) be the complex Lie group of holomorphic automorphisms of X. It is well-known that the dimension of Aut(X) is bounded by an integer that depends only on n=dim
X. Moreover, if X is K?hler then dimAut (X)≤n(n+2) with equality only when X is complex projective space. In this article examples of non-K?hler compact complex homogeneous manifolds X are given that demonstrate dimAut(X) can depend exponentially on n.
Let X be a connected compact complex manifold of dimension n. The group of holomorphic automorphisms of X, Aut(X), is a complex Lie group [3]. For a fixed n>1, the dimension of Aut(X) can be arbitrarily large compared to n. Simple examples are provided by the Hirzebruch surfaces F
m
, m∈N, for which dimAut(F
m
)=m+5, see, e.g. [2, Example 2.4.2].
If X is homogeneous, that is, any point of X can be mapped to any other point of X under a holomorphic automorphism, then the dimension of the automorphism group of X is bounded by an integer that depends only on n, see [1, 2, 6]. The estimate given in [2, Theorem 3.8.2] is roughly dimAut(X)≤(n+2)
n
. For many classes of manifolds, however, the dimension of the automorphism group never exceeds n(n+2). For example, it follows directly from the classification given by Borel and Remmert [4], that if X is a compact homogeneous K?hler manifold, then dimAut(X)≤n(n+2) with equality only when X is complex projective space P
n
. It is an old question raised by Remmert, see [2, p. 99], [6], whether this same bound applies to all compact complex homogeneous
manifolds.
In this note we show that this is not the case by constructing non-K?hler compact complex homogeneous manifolds whose automorphism
group has a dimension that depends exponentially on n. The simplest case among these examples has n=3m+1 and dimAut(X)=3m+3
m
, so the above conjectured bound is exceeded when n≥19. These manifolds have the structure of non-trivial fiber bundles over products of flag manifolds with parallelizable fibers
given as the quotient of a solvable group by a discrete subgroup. They are constructed using the original ideas of Otte [6,
7] and are surprisingly similar to examples found there. Generally, a product of manifolds does not result in an automorphism
group with a large dimension relative to n. Nevertheless, products are used in an essential way in the construction given here, and it is perhaps this feature that
caused such examples to be previously overlooked.
Oblatum 13-X-97 & 24-X-1997 相似文献
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In this paper we completely classify the linearly full homogeneous holomorphic two-spheres in the complex Grassmann manifolds and . We also obtain the Gauss equation for the holomorphic immersions from a Riemann surface into . By using which, we give explicit expressions of the Gaussian curvature and the square of the length of the second fundamental form of these homogeneous holomorphic two-spheres in and . 相似文献
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Kai Lorentz 《Integral Equations and Operator Theory》1989,12(3):435-443
For Jordan elementsJ in a topological algebraB with unite, an open groupB
–1 of invertible elements and continuous inversion we consider the similarity orbitsS
G
(J)={gJg
–1:gG} (G the groupB
–1{e+c:cI},IB a bilateral continuous embedded topological ideal). We construct rational local cross sections to the conjugation mapping
and give to the orbitS
G
(J) the local structure of a rational manifold. Of particular interest is the caseB=L(H) (bounded linear operators on a separable Hilbert spaceH),I=B, for which we obtain the following:
相似文献
1. | If for a Hilbert space operator there exist norm continuous local similarity cross sections, then these can be chosen to be rational, especially holomorphic or real analytic. |
2. | The similarity orbit of a nice Jordan operator is a rational (especially holomorphic or real analytic) submanifold ofL(H). |