A complex map with complex topology

We construct a simple example of a complex algebraic map, which (even locally) has an uncountable number of local topological types at points of the source space.

     

Almost complex structures on connected sums of almost complex manifolds and complex projective spaces

Archiv der Mathematik - For a smooth curve C in $${{\mathbb {P}}}^{r_0}$$ lying on a rational surface scroll, we try to identify those complete and base point free linear series of small degree...     

Almost complex rigidity of the complex projective plane

An isomorphism of symplectically tame smooth pseudocomplex structures on the complex projective plane which is a homeomorphism and differentiable of full rank at two points is smooth.

     

Intrinsic characterizations for complex hypercylinders and complex hyperspheres

In terms of conditions on the curvature tensors of Riemann-Christoffel, Ricci, Weyl and Bochner we obtain several new characterizations of complex hyperspheres in complex projective spaces, of complex hypercylinders in complex Euclidean spaces and of complex hyperlanes in complex space forms.Aspirant N.F.W.O. (België).     

On complex analytic compactifications of complex parallelizable manifolds

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     

Torsion in the matching complex and chessboard complex

Topological properties of the matching complex were first studied by Bouc in connection with Quillen complexes, and topological properties of the chessboard complex were first studied by Garst in connection with Tits coset complexes. Björner, Lovász, Vre?ica and ?ivaljevi? established bounds on the connectivity of these complexes and conjectured that these bounds are sharp. In this paper we show that the conjecture is true by establishing the nonvanishing of integral homology in the degrees given by these bounds. Moreover, we show that for sufficiently large n, the bottom nonvanishing homology of the matching complex Mn is an elementary 3-group, improving a result of Bouc, and that the bottom nonvanishing homology of the chessboard complex Mn,n is a 3-group of exponent at most 9. When , the bottom nonvanishing homology of Mn,n is shown to be Z₃. Our proofs rely on computer calculations, long exact sequences, representation theory, and tableau combinatorics.     

Reducibility of complex submanifolds of the complex euclidean space

Let M be a simply connected complex submanifold of . We prove that M is irreducible, up a totally geodesic factor, if and only if the normal holonomy group acts irreducibly. This is an extrinsic analogue of the well-known De Rham decomposition theorem for a complex manifold. Our result is not valid in the real context, as it is shown by many counter-examples. Received December 1, 1998; in final form March 31, 1999 / Published online July 3, 2000     

Almost complex and complex structures on real projective Stiefel manifolds

We give a complete list of real projective Stiefel manifolds which admit almost complex structures and show that many of them are in fact complex manifolds. The first named author was supported in part by Grants 1/1486/94 and 2/1225/96 of VEGA (Slovakia) during the preparation of this work.     

Flat slant surfaces in complex projective and complex hyperbolic planes

For surfaces in complex space forms with almost complex structure J, flat surfaces are the simplest ones from intrinsic point of view. From J-action point of view, the most natural surfaces are slant surfaces. The classification of flat slant surfaces in C² was done in [2]. In this paper we apply a result of [5] to study flat slant surfaces in CP ² and CH ². We prove that, for any θ, there exist infinitely many flat θ-slant surfaces in CP ² and CH ². And there does not exist flat half-minimal proper slant surface in CP ² and in CH ².     

Differential topology of quotients of complex surfaces by complex conjugation

The paper contains a brief survey of the author’s results on the diffeomorphism type of quotients of complex surfaces by anti-holomorphic involutions. The conjecture of complete decomposability is discussed, which says that if such a quotient is simply connected, then it is completely decomposable, i.e., is diffeomorphic to the connected sum of several copies of the projective plane (possibly, with reversed orientation) and the quadric. Bibliography: 11 titles. Translated fromZapiski Nauchnykh Seminarov POMI, Vol. 231, 1995, pp. 215–221. Translated by O. A. Ivanov.     

复赋范空间中复RS集的最佳同时逼近

研究了复赋范空间中具限制系数的广义多项式集G对无穷序列的最佳同时逼近问题,得到了特征定理;当G是复RS集时还得到了惟一性定理．     

The Mizohata complex

This paper deals with the local solvability of systems of first order linear partial differential equations defined by a germ at of a -valued, formally integrable (), 1-form with nondegenerate Levi form. More precisely, the size of the obstruction to the solvability, for -forms , of the equation

where is a given -form satisfying is estimated in terms of the De Rham cohomology relative to

     

Bordered complex Hessians

We record some basic facts about bordered complex Hessians and logarithmically plurisubharmonic functions. These enable us to prove that a nonnegative bihomogeneous polynomial is plurisubharmonic if and only if it is log-plurisubharmonic; we give a more general version for twice differentiable bihomogeneous functions. The proof relies on the vanishing of the determinant of the bordered complex Hessian; we go on to find general classes of solutions to the nonlinear PDE given by setting the determinant of a bordered complex Hessian equal to zero.     

Bootstrapping complex functions

We formulate a new family of bootstrap algorithms suitable for learning non-Boolean functions from data. Within the Algorithmic Inference framework, the key idea is to consider a population of functions that are compatible with the observed sample. We generate items of this population from standard random seeds and reverse seed probabilities on the items. In this way we may compute in principle, and effectively achieve on paradigmatic examples, direct estimates and confidence intervals for any kind of complex function underlying the observed data according to any hypothesis on the randomness affecting the sample.