相关论文: Hyperbolic surfaces in ${\bf P}^3$: examples
These are lecture notes of a course held at IMPA, Rio de Janiero, in september 2010: the purpose was to present recent results on Kobayashi hyperbolicity in complex geometry. Our ultimate goal is to describe the results obtained on…
We modify the deformation method explored previously in a joint work of B. Shiffman and the author, in order to construct further examples of Kobayashi hyperbolic surfaces in the projective 3-space of any even degree starting with degree 8.
We construct new examples of Kobayashi hyperbolic hypersurfaces in the projective 4-space. They are generic projections of the triple symmetric product of a generic curve of genus at least 7, smoothly embedded in the projective 7-space.
We describe a new method of constructing Kobayashi-hyperbolic surfaces in complex projective 3-space based on deforming surfaces with a "hyperbolic non-percolation" property. We use this method to show that general small deformations of…
The main goal of this work is to prove that a very generic surface of degree at least 21 in complex projective 3-dimensional space is hyperbolic in the sense of Kobayashi. This means that every entire holomorphic map $f:{\Bbb C} \to X$ to…
We construct two classes of singular Kobayashi hyperbolic surfaces in $P^3$. The first consists of generic projections of the cartesian square $V = C \times C$ of a generic genus $g \ge 2$ curve $C$ smoothly embedded in $P^5$. These…
We show that a general small deformation of the union of two general cones in P3 of degree >= 4 is Kobayashi hyperbolic. Hence we obtain new examples of hyperbolic surfaces in P3 of any given degree d>= 8.
We present two methods of constructing low degree Kobayashi hyperbolic hypersurfaces in the projective space: the projection method and the deformation method. The talk is based on joint works of the speaker with B. Shiffman and C.…
The paper is a contribution to the conjecture of Kobayashi that the complement of a generic curve in the projective plane is hyperbolic, provided the degree is at least five. Previously the authors treated the cases of two quadrics and a…
In 1970, Kobayashi conjectured that general hypersurfaces of sufficiently large degree in $P^n$ are hyperbolic. In this paper we prove that a general sufficiently ample hypersurface in a smooth projective variety is hyperbolic. To prove…
In this article we study the injective Kobayashi metric on complex surfaces.
In this paper, we prove that in any projective manifold, the complements of general hypersurfaces of sufficiently large degree are Kobayashi hyperbolic. We also provide an effective lower bound on the degree. This confirms a conjecture by…
For a generic hypersurface $\mathbb{X}^{n-1} \subset \mathbb{P}^n(\mathbb{C})$ of degree \[ d \,\geqslant\, n^{2n} \] (1) $\mathbb{P}^n \big\backslash \mathbb{X}^{n-1}$ is Kobayashi-hyperbolically imbedded in $\mathbb{P}^n$; (2)…
Oka manifolds can be viewed as the "opposite" of Kobayashi hyperbolic manifolds. Kobayashi asked whether the complement in projective space of a generic hypersurface of sufficiently high degree is hyperbolic. Therefore it is natural to…
We first give a sufficient condition, issued from pluripotential theory, for an unbounded domain in the complex Euclidean space $\mathbb C^n$ to be Kobayashi hyperbolic. Then, we construct an example of a rigid pseudoconvex domain in…
Generalizing both hyperbolic framed surfaces and one-parameter families of hyperbolic framed curves, we introduce the concept of hyperbolic generalized framed surfaces and establish their relations in hyperbolic 3-space. We provide the…
This is the third in a series of papers constructing hyperbolic structures on all Haken three-manifolds. This portion deals with the mixed case of the deformation space for manifolds with incompressible boundary that are not acylindrical,…
The paper is a contribution of the conjecture of Kobayashi that the complement of a generic plain curve of degree at least five is hyperbolic. The main result is that the complement of a generic configuration of three quadrics is hyperbolic…
We construct examples of inhomogeneous isoparametric real hypersurfaces in complex hyperbolic spaces.
We survey the properties of Brody and Kobayashi hyperbolic manifolds.