## What is the degree of a vector bundle?

We want to give a definition of degree for vector bundles. With the correspondence between divisors and line bundles, we define the degree of a line bundle as the degree of its associated divisor.

## What is a positive line bundle?

A holomorphic line bundle on a complex manifold is called positive if its curvature differential 2-form is, after multiplication with i=√−1, a positive definite (1,1)-form.

**What is an ample line bundle?**

A line bundle is ample if some positive power is very ample. An ample line bundle on a projective variety X has positive degree on every curve in X. The converse is not quite true, but there are corrected versions of the converse, the Nakai–Moishezon and Kleiman criteria for ampleness.

### What is a trivial bundle?

A bundle or fiber bundle is trivial if it is isomorphic to the cross product of the base space and a fiber.

### What is a section of a vector bundle?

A bundle section of a vector bundle is a map whose projection, is the identity map on . For instance, on a trivial bundle , a section corresponds to a function by . Near every point in a vector bundle, there is a trivialization. The structure of the vector bundle, as in all bundles, is that it is locally trivial.

**What does ample mean?**

Definition of ample 1 : generous or more than adequate in size, scope, or capacity There was room for an ample garden. 2 : generously sufficient to satisfy a requirement or need They had ample money for the trip.

## Is a vector bundle a fiber bundle?

A special class of fiber bundles, called vector bundles, are those whose fibers are vector spaces (to qualify as a vector bundle the structure group of the bundle — see below — must be a linear group). Important examples of vector bundles include the tangent bundle and cotangent bundle of a smooth manifold.

## What is a fiber bundle math?

A fiber bundle (also called simply a bundle) with fiber is a map where is called the total space of the fiber bundle and the base space of the fiber bundle. The main condition for the map to be a fiber bundle is that every point in the base space has a neighborhood such that is homeomorphic to in a special way.

**What is a bundle in math?**

Bundling is also called grouping. This is a way to group numbers by putting the smaller units together to make a larger one. For instance, putting 10 ones together makes 1 ten. Putting 10 tens together makes 1 hundred. Counting using Base Ten.

### What is a Canuckle?

The brainchild of Ottawa resident, Mark Rogers, Canuckle is a Wordle-based guessing game that challenges the player to guess a five-letter word that in some way relates to Canada. The mystery word could be anything from a word, place, or simple Canadianism – if it’s tied to Canada, it goes.

### What are Bussums?

1a : the human chest and especially the front part of the chest hugged the child to his bosom. b : a woman’s breasts regarded especially as a single feature a woman with an ample bosom also : breast a woman’s bosoms.

**Are bundles manifolds?**

Differentiable fiber bundles is called a fibered manifold.

## What is the degree of a line bundle on a curve?

The degree of a line bundle L on a proper curve C over k is defined as the degree of the divisor (s) of any nonzero rational section s of L. The coefficients of this divisor are positive at points where s vanishes and negative where s has a pole. Therefore, any line bundle L on a curve C such that

## What is a line bundle in math?

In mathematics, a line bundle expresses the concept of a line that varies from point to point of a space. For example, a curve in the plane having a tangent line at each point determines a varying line: the tangent bundle is a way of organising these.

**When is a line bundle ample?**

More strongly, a line bundle on X is very ample if it has enough sections to give a closed immersion (or “embedding”) of X into projective space. A line bundle is ample if some positive power is very ample.

### When is a line bundle globally generated?

A line bundle is globally generated if and only if it is basepoint-free. For example, every quasi-coherent sheaf on an affine scheme is globally generated. Analogously, in complex geometry, Cartan’s theorem A says that every coherent sheaf on a Stein manifold is globally generated.