Search results
Results From The WOW.Com Content Network
Download as PDF; Printable version; In other projects ... In algebraic geometry, if : is a morphism of schemes, the fiber of a point in is the fiber product ...
The choice of a (normalised) cleavage for a fibred -category specifies, for each morphism : in , a functor:; on objects is simply the inverse image by the corresponding transport morphism, and on morphisms it is defined in a natural manner by the defining universal property of cartesian morphisms.
In the field of mathematics known as algebraic topology, the Gysin sequence is a long exact sequence which relates the cohomology classes of the base space, the fiber and the total space of a sphere bundle. The Gysin sequence is a useful tool for calculating the cohomology rings given the Euler class of the sphere bundle and vice versa.
In mathematics, a bundle map (or bundle morphism) is a morphism in the category of fiber bundles. There are two distinct, but closely related, notions of bundle map, depending on whether the fiber bundles in question have a common base space. There are also several variations on the basic theme, depending on precisely which category of fiber ...
In algebraic geometry, the Stein factorization, introduced by Karl Stein for the case of complex spaces, states that a proper morphism can be factorized as a composition of a finite mapping and a proper morphism with connected fibers. Roughly speaking, Stein factorization contracts the connected components of the fibers of a mapping to points.
A morphism f : X → Y is called an isomorphism if there exists a morphism g : Y → X such that f ∘ g = id Y and g ∘ f = id X. If a morphism has both left-inverse and right-inverse, then the two inverses are equal, so f is an isomorphism, and g is called simply the inverse of f. Inverse morphisms, if they exist, are unique.
Then there is a morphism Spec(k(y)) → Y with image y, where k(y) is the residue field of y. The fiber of f over y is defined as the fiber product X × Y Spec(k(y)); this is a scheme over the field k(y). [3] This concept helps to justify the rough idea of a morphism of schemes X → Y as a family of schemes parametrized by Y.
In geometry and topology, given a group G (which may be a topological or Lie group), an equivariant bundle is a fiber bundle: such that the total space and the base space are both G-spaces (continuous or smooth, depending on the setting) and the projection map between them is equivariant: = with some extra requirement depending on a typical fiber.