Related papers: Holomorphic maps from complex discs intersecting f…
Among Thurston maps (orientation-preserving, postcritically finite branched coverings of the 2-sphere to itself), those that arise as subdivision maps of a finite subdivision rule form a special family. For such maps, we investigate…
We give a necessary and sufficient condition for the existence of nondegenerate holomorphic mappings between pseudoellipsoidal real hypersurfaces, and provide an explicit parametrization for the collection of all such mappings (in the…
We study fixed point sets for holomorphic automorphisms (and endomorphisms) on complex manifolds. The main object of our interest is to determine the number and configuration of fixed points that forces an automorphism (endomorphism) to be…
The main two families of real hypersurfaces in complex space forms are Hopf and ruled. However, very little is known about real hypersurfaces in the indefinite complex projective space $\cpn$. In a previous work, Kimura and the second…
For a projective hypersurface $X \subset \P^n$, the images of the polar maps of degree $k$ are studied. The cohomology class defined by these maps is calculated and classical results on dual varieties are presented as applications.
We characterize those regular, holomorphic or formal maps into the orbit space $V/G$ of a complex representation of a finite group $G$ which admit a regular, holomorphic or formal lift to the representation space $V$. In particular, the…
The purpose of this article is to deal with the multiple values and uniqueness problem of meromorphic mappings from $\mathbb{C}^{m}$ into the complex projective space $\mathbb{P}^{n}(\mathbb{C})$ sharing fixed and moving hypersurfaces. We…
In this paper, by introducing the notion of "\textit{distributive constant}" of a family of hypersurfaces with respect to a projective variety, we prove a second main theorem in Nevanlinna theory for meromorphic mappings with arbitrary…
We consider complex dynamics of a critically finite holomorphic map from P^k to P^k, which has symmetries associated with the symmetric group S_{k+2} acting on P^k, for each k \ge 1. The Fatou set of each map of this family consists of…
In one complex variable it is well known that if we consider the family of all holomorphic functions on the unit disc that fix the origin and with first derivative equal to 1 at the origin, then there exists a constant $\rho$, independent…
We prove that the set of leaves of a holomorphic lamination of codimension one that are non-transversal to a germ of a holomorphic map is discrete.
In this note, we prove a rigidity result for proper holomorphic maps between unit balls that have many symmetries and which extend to $\mathcal{C}^2$-smooth maps on the boundary.
We investigate the geometry of holomorphic curves and complex surfaces from the perspective of singularity theory. We show that, with a suitable choice of a complex bilinear symmetric form, the families of functions and mappings that…
Generalising an example by Girondo and Wolfart, we use finite group theory to construct Riemann surfaces admitting two or more regular dessins (i.e. orientably regular hypermaps) with automorphism groups of the same order, and in many cases…
We investigate the value distribution of holomorphic maps defined on one class of K\"ahler manifolds. With the very natural settings, we establish a Second Main Theorem which is of the similar form as ones of the classical Second Main…
For a finite set $S$ of points in the plane and a graph with vertices on $S$ consider the disks with diameters induced by the edges. We show that for any odd set $S$ there exists a Hamiltonian cycle for which these disks share a point, and…
In this article we completely determine the possible dimensions of integral points and holomorphic curves on the complement of a union of hyperplanes in projective space. Our main theorems generalize a result of Evertse and Gyory, who…
The explicit form of proper holomorphic mappings between complex ellipsoids is given. Using this description, we characterize the existence of proper holomorphic mappings between generalized Hartogs triangles and give their explicit form.…
We study pseudoholomorphic discs with boundaries attached to a real hypersurface in an almost complex manifold. We give sufficient conditions for filling a one sided neighborhood of the hypersurface by the discs.
We estimate the dimensions of the spaces of holomorphic sections of certain line bundles to give improved lower bounds on the index of complex isotropic harmonic maps to complex projective space from the sphere and torus, and in some cases…