Related papers: Fibers and global geometry of functions

Inspired by the work of Ellenberg, Elsholtz, Hall, and Kowalski, we investigate how the property of the generic fiber of a one-parameter family of abelian varieties being geometrically simple extends to other fibers. In \cite{EEHK09}, the…

Controlled algebra plays a central role in many recent advances in geometric topology. This paper studies the iteration construction that was present from the very origins of the theory but started being exploited only recently. We develop…

Inspired by the recent algebraic approach to classical field theory, we propose a more general setting based on the manifold of smooth sections of a non-trivial fiber bundle. Central is the notion of observables over such sections, i.e.…

We introduce the notion of Fermi flow for hypersurfaces in Riemannian manifolds. It turns out that this is a powerful tool to study the geometry of distance surfaces about a given initial hypersurface. Some of the results in this paper are…

We develop a categorical framework for reasoning about abstract properties of differentiation, based on the theory of fibrations. Our work encompasses the first-order fragments of several existing categorical structures for differentiation,…

The paper gives a categorical approach to generalized manifolds such as orbit spaces and leaf spaces of foliations. It is suggested to consider these spaces as sets equipped with some additional structure which generalizes the notion of…

Let $\mathcal{X}\rightarrow C$ be a dominant morphism between smooth irreducible varieties over a finitely generated field $k$ such that the generic fiber $X$ is smooth, projective and geometrically connected. Assuming that $C$ is a curve…

We introduce the notion of an enriched fibration, i.e. a fibration whose total category and base category are enriched in those of a monoidal fibration in an appropriate way. Furthermore, we provide a way to obtain such a structure,…

Much information about a graph can be obtained by studying its spanning trees. On the other hand, a graph can be regarded as a 1-dimensional cell complex, raising the question of developing a theory of trees in higher dimension. As observed…

We recall the history of the proof of Seifert fibre space conjecture, as well as it motivations and its several generalisations.

In this short note we prove the Iitaka C_nm conjecture for algebraic fiber spaces over surfaces

This is an introduction to Grothendieck's descent theory, with some stress on the general machinery of fibered categories and stacks.

This is the fourth of a series of papers studying real algebraic threefolds, but the methods are mostly independent from the previous ones. Let $f:X\to C$ be a map of a smooth projective real algebraic 3-fold to a curve $C$ whose general…

In this paper we introduce the notion of Hurewicz fibrations in the class of embedding maps of orbifold charts by giving the concept of E-fibration embedding. We study the fundamental properties of this concept such as the restriction,…

We study linear functions on fibrations whose central fibre is a linear free divisor. We analyse the Gauss-Manin system associated to these functions, and prove the existence of a primitive and homogenous form. As a consequence, we show…

In this Master of Science Thesis I introduce geometric algebra both from the traditional geometric setting of vector spaces, and also from a more combinatorial view which simplifies common relations and operations. This view enables us to…

The purpose of this paper is to present a generalized hole argument for gauge field theories and their geometrical setting in terms of fiber bundles. The generalized hole argument is motivated and extended from the spacetime hole arguments…

We use the theory of foliations to study the relative canonical divisor of a normalized inseparable base-change. Our main technical theorem states that it is linearly equivalent to a divisor with positive integer coefficients divisible by…

We extend Michel's theorem on the geometry of symmetry breaking [L. Michel, {\it Comptes Rendus Acad. Sci. Paris} {\bf 272-A} (1971), 433-436] to the case of pure gauge theories, i.e. of gauge-invariant functionals defined on the space…

By recasting metrical geometry in a purely algebraic setting, both Euclidean and non-Euclidean geometries can be studied over a general field with an arbitrary quadratic form. Both an affine and a projective version of this new theory are…