Related papers: About the hyperbolicity of complete intersections

Firstly, we pursue the work of W. Cherry on the analogue of the Kobayashi semi distance dCK that he introduced for analytic spaces defined over a non-Archimedean metrized field k. We prove various characterizations of smooth projective…

We give two new elementary proofs of the complete Kobayashi hyperbolicity of the twice-punctured complex plane. We also present an extremely short proof that bounded domains are complete Kobayashi hyperbolic. Our proofs rely neither on the…

This paper represents an elaboration of the lectures delivered by one of us (CAF) during "Course 197 -- Foundations of Quantum Physics" at the International School of Physics "Enrico Fermi" in Varenna, Italy, July 2016. Much of the material…

This survey discusses hyperbolicity properties of moduli stacks and generalisations of the Shafarevich Hyperbolicity Conjecture to higher dimensions. It concentrates on methods and results that relate moduli theory with recent progress in…

We survey the properties of Brody and Kobayashi hyperbolic manifolds.

This is an expanded and updated version of the talk I gave at the meeting organized at CERN on April 27-28, 2015 dedicated to honoring the memory of Bruno Zumino and his legacy. In this talk I review the emergence of exceptional structures…

The aim of this work is to construct examples of pairs whose logarithmic cotangent bundles have strong positivity properties. These examples are constructed from any smooth n-dimensional complex projective varieties by considering the sum…

This note is an expansion of three lectures given at the workshop "Topology, Complex Analysis and Arithmetic of Hyperbolic Spaces" held at Kyoto University in December of 2006 and will appear in the proceedings for this workshop.

We prove that elliptic tubes over properly convex domains of the real projective space are C-convex and complete Kobayashi-hyperbolic. We also study a natural construction of complexification of convex real projective manifolds.

We give conditions for $f$-positivity of relative complete intersections in projective bundles. We also derive an instability result for the fibres.

We introduce the notions of geometric height and graded (geometric) relative hyperbolicity in this paper. We use these to characterize quasiconvexity in hyperbolic groups, relative quasiconvexity in relatively hyperbolic groups, and convex…

We study the hyperbolicity properties of moduli spaces of marked hyperk{\"a}hler manifolds along directions corresponding to families having positivity properties for their Hodge bundle. In particular, we show that the Kobayashi…

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.…

In this article we prove that the complement of a very generic curve of degree at least equal to 14 in the complex projective plane is hyperbolic in the sense of Kobayashi. Thus, using a new method, we improve the former known bound…

These notes reproduce the content of a short, 50-minutes, survey talk given at the Nice University in September, 2004. We added a few topics that have not been touched on in the lecture by lack of time.

Using the Donaldson-Auroux theory, we construct complete intersections in complex projective manifolds, which are negatively curved in various ways. In particular, we prove the existence of compact simply connected Kahler manifolds with…

We prove an analogue of the Brody lemma in the framework of Riemannian manifolds. We also present new examples of Riemannian manifolds that are hyperbolic in the sense of Kobayashi.

This is the written version of a talk given in Bonn on September 11th, 2001 during a workshop on "Special structures in string theory". We report on joint work in progress with George Papadopoulos aimed at classifying the maximally…

We review various combinatorial problems with underlying classical or quantum integrable structures. (Plenary talk given at the International Congress of Mathematical Physics, Aalborg, Denmark, August 10, 2012.)

The paper is an extended version of the talk which I gave at the XIX Congresso dell'UMI in Bologna in September 2011. The aim of this paper is twofold: first, to give an overview on the recent development in the classification of surfaces…