Related papers: About the hyperbolicity of complete intersections
We discuss the notion of the universal relatively hyperbolic structure on a group which is used in order to characterize relatively hyperbolic structures on the group. We also study relations between relatively hyperbolic structures on a…
We discuss two properties of an abelian variety, namely, being a direct summand in a product of Jacobians and the weaker property of being "split". We relate the first property to the integral Hodge conjecture for curve classes on abelian…
In this paper, we provide two different resolutions of structural sheaves of projectivized tangent bundles of smooth complete intersections. These resolutions allow in particular to obtain convenient (and completely explicit) descriptions…
If G_0 is a real form of a complex semisimple Lie group G and Z is compact G-homogeneous projective algebraic manifold, then G_0 has only finitely many orbits on Z. Complex analytic properties of open G_0-orbits D (flag domains) are…
Looking at the finite \'etale congruence covers $X(p)$ of a complex algebraic variety $X$ equipped with a variation of integral polarized Hodge structures whose period map is quasi-finite, we show that both the minimal gonality among all…
This paper is Part III of a series of three. We begin by introducing the notion of $h$-special varieties, which can be seen as varieties "chain-connected by the Zariski closures of entire curves." We prove that if $X$ is either a special…
This talk is dedicated to various aspects of Mirror Symmetry. It summarizes some of the mathematical developments that took place since M. Kontsevich's report at the Z\"urich ICM and provides an extensive, although not exhaustive,…
We introduce the notion of topological hyperbolicity to characterize the largeness of the topological fundamental group of a complex variety. Inspired by the Shafarevich conjecture, we propose to study the topological hyperbolicity of…
We equate dynamical properties (e.g., positive entropy, existence of a periodic curve) of complex projective surface automorphisms with properties of the pull-back actions of such automorphisms on line bundles. We use the properties of the…
The magnetic Laplacian on hyperbolic surfaces provides a rich analytic framework in which a variety of quantum phenomena emerge. The present note, written for the \emph{Proceedings of the Journ\'ees EDP 2025}, is a concise overview of the…
We compute and analyse the moduli space of those real projective structures on a hyperbolic 3-orbifold that are modelled on a single ideal tetrahedron in projective space. Parameterisations are given in terms of classical invariants,…
An elementary review of models and phenomenology for physics beyond the Standard Model (excluding supersymmetry). The emphasis is on LHC physics. Based upon a talk given at the Physics at LHC conference, Vienna, 13-17 July 2004.
We show the following algebraicity result for a complex projective variety $X$ with big representation of $\pi_1$ into a semi-simple algebraic group: There exists a proper subvariety $Z \subset X$ such that for any algebraic curve $C$, any…
The article is a slightly extended version of the talk, with the same title, which I gave at the Kinosaki Symposium on Algebraic Geometry in October 2011, and dealing with the classification of complex projective surfaces of general type…
The lack of a uniformization theorem in several complex variables leads to a desire to classify all of the simply connected domains. We use established computational methods and a localization technique to generalize a recently-published…
We study the existence and regularity of invariant graphs for bundle maps (or bundle correspondences with generating bundle maps motivated by ill-posed differential equations) having some relative partial hyperbolicity on non-trivial and…
We show that, over a local complete intersection, every possible variety is realized as the cohomological support variety of some module. Moreover, we show that the projective variety of a complete indecomposable maximal Cohen-Macaulay…
This is the story of the rediscovery of classical three-dimensional geometry, especially the geometry of quadric surfaces, while studying the semigroup $M_2(\mathbb R)$ of linear endomorphisms of a real plane. One of the surfaces that…
This is an extended abstract for the conference "Microlocal2011 : Microlocal Methods in Mathematical Physics and Global Analysis Universitat Tubingen, June 14 - 18, 2011"
This is an expanded version of the author's lecture at the Conference in Commutative Algebra and Algebraic Geometry in Messina Italy in June 1999. The purpose of the talk was to give a brief introduction to the subject of tight closure,…