Related papers: On ampleness of canonical bundle
We study fundamental groups of non compact Riemannian manifolds. We find conditions which ensure that the fundamental group is trivial, finite or finitely generated.
After a historical discussion of classical uniformisation results for Riemann surfaces, of problems appearing in higher dimensions, and of uniformisation results for projective manifolds with trivial or ample canonical bundle, we introduce…
We prove several finiteness theorems for the normal bundles to souls in nonnegatively curved manifolds. More generally, we obtain finiteness results for open Riemannian manifolds whose topology is concentrated on compact domains of…
The cotangent bundle of a non-uniruled projective manifold is generically nef, due to a theorem of Miyaoka. We show that the cotangent bundle is actually generically ample, if the manifold is of general type and study in detail the case of…
We study the geometry of projective manifolds whose tangent bundles are nef on sufficiently general curves (i.e. the tangent bundle is generically nef) and show that manifolds whose anticanonical bundles are semi-ample have this property.…
We extend the Colombeau algebra of generalized functions to arbitrary (infinitely differentiable, paracompact) n-dimensional manifolds M. Embedding of continuous functions and distributions is achieved with the help of a family of n-forms…
Theorem (uniformization). Let X be a compact Kahler manifold of dimension n with large, residually finite and nonamenable fundamental group. Then its universal covering is a bounded domain in the n-dimensional affine space.
We present here some conjectures on the diagonalizability of uniform principal bundles on rational homogeneous spaces, that are natural extensions of classical theorems on uniform vector bundles on the projective space, and study the…
Projective spaces for finite-dimensional vector spaces over general fields are considered. The geometry of these spaces and the theory of line bundles over these spaces is presented. Particularly, the space of global regular sections of…
A theory of principal bundles possessing quantum structure groups and classical base manifolds is presented. Structural analysis of such quantum principal bundles is performed. A differential calculus is constructed, combining differential…
We show that the canonical central extension of the group of sections of a Lie group bundle over a compact manifold, constructed in [NW09], is universal. In doing so, we prove universality of the corresponding central extension of Lie…
Co lombeau's construction of generalized functions (in its special variant) is extended to a theory of generalized sections of vector bundles. As particular cases, generalized tensor analysis and exterior algebra are studied. A point value…
This article generalises to K\"ahler orbifolds general results on uniformisation of compact K\"ahler manifolds such as the Shafarevich conjecture for linear fundamental groups.
We prove a conjecture of Shafarevich about universal coverings of projective manifolds provided the fundamental group is residually finite.
We prove a canonical bundle formula for generically finite morphisms in the setting of generalized pairs (with $\mathbb{R}$-coefficients). This complements Filipazzi's canonical bundle formula for morphisms with connected fibres. It is then…
We prove that every nontrivial principal $G_m$-bundle over a complete uniformly rational variety is algebraically elliptic in the sense of Gromov.
Apart from math.AG/0608569, it contains the following applications of it. Let M be a simply connected, irreducible smooth complex projective variety of dimension $n$ such that the Picard number of $M$ is one. If the canonical line bundle…
A general noncommutative-geometric theory of principal bundles is presented. Quantum groups play the role of structure groups. General quantum spaces play the role of base manifolds. A differential calculus on quantum principal bundles is…
A noncommutative-geometric generalization of the classical formalism of frame bundles is developed, incorporating into the theory of quantum principal bundles the concept of the Levi-Civita connection. The construction of a natural…
Let U be a universal covering of a connected nonsingular projective variety X with large and residually finite fundamental group. We construct metrics on U and provide another version of the uniformization theorem, namely: if the…