Related papers: Concrete fibrations
We give an elementary construction of the dual fibration of a fibration. It does not use the non-elementary notion of (pseudo-) functor into the category of categories.
We describe the construction of the slice fibration of a given one.
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,…
We discuss the flatness property of some fiber type contractions of complex smooth projective varieties of arbitrary dimensions. We relate the flatness of some morphisms having one-dimensional fibers with their conic bundles structures,…
We give a simple diagrammatic proof of the Frobenius property for generic fibrations, that does not depend on any additional structure on the interval object such as connections.
In this short expository note, we discuss, with plenty of examples, the bestiary of fibrations in quasicategory theory. We underscore the simplicity and clarity of the constructions these fibrations make available to end-users of higher…
It is known that the paving conjecture fails for 2-paving projections with constant diagonal 1/2. But the proofs of this fact are existence proofs. We will give concrete examples of these projections and projections with constant diagonal…
We investigate the existence, and lack of unicity, of a holomorphic fibration by discs transversal to a rational curve in a complex surface.
We discuss the existence and non-existence of cobordisms between symplectic surface bundles over the circle.
In this note we define fibrations of topological stacks and establish their main properties. We prove various standard results about fibrations (fiber homotopy exact sequence, Leray-Serre and Eilenberg-Moore spectral sequences, etc.). We…
Definability is a key notion in the theory of Grothendieck fibrations that characterises when an external property of objects can be accessed from within the internal logic of the base of a fibration. In this paper we consider a…
In this article, we discuss some properties of holomorphic fibrations in the complex analytic setting.
Discussion of physical realization of coordinates demonstrates that the quantum theory of gravity (still absent) should be non-local and, probably, non-commutative as well.
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…
We classify elliptic fibrations birational to a nonsingular, minimal cubic surface over a field of characteristic zero. Our proof is adapted to provide computational techniques for the analysis of such fibrations, and we describe an…
We construct examples of simply connected surfaces with genus 2 fibrations over the projective line which are of "general type" according to the definition of Campana. These fibrations have special fibres such that the minimum of the…
This survey describes some recent work, by the authors and others, on the existence of algebraic fibrations of group extensions, as well as the finiteness properties of their algebraic fibers, in the realm of both abstract and pro-$p$…
An elementary theory of strict $\infty $-categories with application to concrete duality is given. New examples of first and second order concrete duality are presented.
The notion of generalized Seifert fibration is introduced, it is shown that the projections of certain Eschenburg $7$-manifolds onto ${\mathbb C} P^2$ define such fibrations, and for them the characteristic classes corresponding to the…
We give a brief survey of the concept of birational rigidity, from its origins in the two-dimensional birational geometry, to its current state. The main ingredients of the method of maximal singularities are discussed. The principal…