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1.
In this paper we establish two results concerning algebraic (,+)-actions on n . First, let be an algebraic (,+)-action on 3. By a result of Miyanishi, its ring of invariants is isomorphic to [t 1,t 2]. Iff 1,f 2 generate this ring, the quotient map of is the mapF:32,x(f 1(x), f2(x)). By using some topological arguments we prove thatF is always surjective. Secon, we are interested in dominant polynomial mapsF: n n-1 whose connected components of their generic fibers are contractible. For such maps, we prove the existence of an algebraic (,+)-action on n for whichF is invariant. Moreover we give some conditions so thatF*([t 1,...,t n-1 ]) is the ring of invariants of .Dedicated to all my friends and my family  相似文献   

2.
We study a nonidentity transvection (i.e. (strictly) hyperbolic isometry) or nonidentity Heisenberg translation f of complex hyperbolic space H n and a Dirichlet polyhedron P of the cyclic group f. We have four main results: (a) If z & in H n and the axis of a nonidentity transvection are not complex collinear, then, roughly speaking, any two distinct 'naturally arising' geodesics passing through z are not complex collinear. (b) If g is also a transvection or Heisenberg translation of H n and z & in H n such that f(z)=g(z) and f –1(z)=g –1(z), then f=g. (c) We classify all this kind of polyhedra up to congruence in H n. (d) We obtain an equivalent condition for P to be cospinal (which means that the complex spines of the two sides of P coincide) in terms of the distance of the spines of the two sides of P.  相似文献   

3.
We consider multivalued analytic functions in n) whose set of singular points occupies a very small part of n). Under a mapping of a topological space Y into n), such a function f can induce a multivalued function on Y. This is possible even if the image of Y entirely lies in the ramification set of f. We estimate the monodromy group of the induced function via the monodromy group of f.  相似文献   

4.
LetV be a finite dimensional complex linear space and letG be a compact subgroup of GL(V). We prove that an orbitG, V, is polynomially convex if and only ifG is closed andG is the real form ofG . For every orbitG which is not polynomially convex we construct an analytic annulus or strip inG with the boundary inG. It is also proved that the group of holomorphic automorphisms ofG which commute withG acts transitively on the set of polynomially convexG-orbits. Further, an analog of the Kempf-Ness criterion is obtained and homogeneous spaces of compact Lie groups which admit only polynomially convex equivariant embeddings are characterized.Supported by Federal program Integratsiya, no. 586.Supported by INTAS grant 97/10170.  相似文献   

5.
A linear geometric order theory for holomorphic mappings F: nm is given if a family of linear subspaces L of n×m is specified; the theory then is concerned with the order number of connected parts of the intersections L (F) of the L's with the graph (F) of F. For m=1 (i.e. case of one function) it is proved that the local linear order number of a holomorphic function is finite in every point. If the L's are real-linear subspaces then real differential geometric methods lead to the proof, if the L's are complex-linear then ideal-theoretical means do.  相似文献   

6.
We show that a closed 4-dimensional simply connected topological manifoldM admits a differentiable structure with aC Riemannian metric whose geodesic flow has zero topological entropy if and only ifM is homeomorphic toS 4, 2,S 2×S 2, or 2#2.  相似文献   

7.
Let : X T be a small deformation of a normal Gorenstein surface singularity X 0 = -1(0) over the complex number field . Suppose that T is a neighborhood of the origin of and that X 0 is not log-canonical. We show that if a topological invariant -P t P t of X t = -1(t) is constant, then, after a suitable finite base change, admits a simultaneous resolution f : M X which induces a locally trivial deformation of each maximal string of rational curves at an end of the exceptional set of M 0 X 0; in particular, if X 0 has a star-shaped resolution graph, then admits a weak simultaneous resolution (in other words, is an equisingular deformation).  相似文献   

8.
Let R be a rational function, of degree 2, with complex coefficients. Then the Julia set of R is a closed subset of 1(), and therefore compact. If one replace by the field p (completion of an algebraic closure of the field p of the p-adic numbers), then one can define also a Julia set for a rational function with p-adic coefficients. But as p is not locally compact, the Julia set may or may not be compact. In this paper, we study the compactness of the Julia set of p-adic polynomials. Mathematics Subject Classification (2000):11S99, 37B99.  相似文献   

9.
We make a contribution to the study of Willmore surfaces infour-dimensional Euclidean space 4 by making useof the identification of 4 with two-dimensionalcomplex Euclidean space 2. We prove that theWhitney sphere is the only Willmore Lagrangian surface of genus zero in4 and establish some existence and uniquenessresults about Willmore Lagrangian tori in 4 2.  相似文献   

10.
It is known that the characterizations of the Toeplitz operatorT onH 2 and also the Hankel operatorH onH 2 by using the simple unilateral shiftT z . Recently, some characterization of the normal Toeplitz matrix truncated on n is given by D.R.Farenick, M. Krupnik, N. Krupnik and W. Y. Lee [1] and, independently, by T.Ito [2]. In this paper, we shall give some characterizations of the Toeplitz matrix and also the Hankel matrix truncated on n .Dedicated to Professor Masanori Fukamiya on his 88th birthday  相似文献   

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