Related papers: Relative internality and definable fibrations
We show that a smooth 1-parameter family of foliations by circles of a closed 3-manifold, deforming the foliation whose leaves are the fibers of a circle bundle, is trivial, i.e. all the foliations of the family arise from circle bundles…
We provide an intrinsic definition of the fundamental group of a linear category over a ring as the automorphism group of the fibre functor on Galois coverings. If the universal covering exists, we prove that this group is isomorphic to the…
In this short note, we introduce a generalization of the canonical base property, called transfer of internality on quotients. A structural study of groups definable in theories with this property yields as a consequence infinitely many new…
In this paper, we give some results on the birational geometry of varieties of Fano type and boundedness problems in positive characteristic, including a result ensuring that boundedness is invariant under normalizations, a canonical bundle…
In the first part of this paper, we propose a uniform interpretation of characteristic classes as obstructions to the reduction of the structure group and to the existence of an equivariant extension of a certain homomorphism defined a…
We establish the generalized canonical bundle formula for generalized lc-trivial fibrations with irrational coefficients over non-compact bases in the complex analytic setting, and we show that the discriminant b-divisor and moduli…
We generalise a theorem on the existence of Frobenius isocrystal and Fontaine-Laffaille module structures on rigid flat connections to the non-proper setting. The proof is based on a new strategy of a point-set topological flavour, which…
Generalizing the $\omega$-categorical context, we introduce a notion, which we call the Lascar Property, that allows for a fine analysis of the topological isomorphisms between automorphism groups of countable structures satisfying this…
We introduce a natural concept of positive definiteness for bundle maps between Fell bundles over (possibly different) discrete groups and describe several examples. Such maps induce completely positive maps between the associated full…
Given any pointed CW complex (X,x), it is well known that the fondamental group of X pointed at x is naturally isomorphic to the automorphism group of the functor which associates to a locally constant sheaf on X its fibre at x. The purpose…
We give an explicit example of a fibration $f \colon X \to Y$ between smooth projective varieties whose "orbifold base" $\Delta_f$ in the sense of Campana has the property that the induced morphism $X \to (Y, \Delta_f)$ is not a morphism of…
A new notion of independence relation is given and associated to it, the class of flat theories, a subclass of strong stable theories including the superstable ones is introduced. More precisely, after introducing this independence…
We introduce a geometric construction of a gauge field theory of a complex adaptive system. It is based on a suitable simplicial formulation of a discrete geometry that manifests relevant properties valid in the classical differentiable…
We classify fibrations by integral plane projective rational quartic curves whose generic fibre is regular but admits a non-smooth point that is a canonical divisor. These fibrations can only exist in characteristic two. The geometric…
Consider a smooth proper holomorphic fibration of complex manifolds. It is known that the semipositivity of the curvature of the direct image of the relative canonical bundle can be read in terms of the cup product with the Kodaira-Spencer…
The aim of the present paper is to investigate new classes of symplectically fat fibre bundles. We prove a general existence theorem for fat vectors with respect to the canonical invariant connections. Based on this result we give new…
Let $R$ be a complete discrete valuation ring with residue characteristic $p>0$. In this note we give an example of a Galois cover $f:Y\to X$ between flat and normal formal $R$-schemes of finite type which is \'etale above the generic fibre…
The underlying mathematical structures of gauge theories are known to be geometrical in nature and the local and global features of this geometry have been studied for a long time in mathematics under the name of fibre bundles. It is now…
In this paper we show that integral fusion categories with rational structure constants admit a natural group of symmetries given by the Galois group of their character tables. We also generalize a well known result of Burnside from…
We address the recently introduced notions of generalized principal bundle and generalized principal connection by keeping track of global geometric properties through local coordinate transformation laws. This approach leads us to…