## Vector Bundle Model |

**For SAEKI Shizuto**

**P**

^{n}is projective space.

**P**

^{1}is projective line.

*E*is vector bundle over

**P**

^{1}.

Theorem (Grothendieck

*)*

Vector bundle E over projective lineVector bundle E over projective line

**P**^{1}is isomorphic withdirect sum of line bundles.
[Note 1]

Language is supposed to be projective space

Word is supposed to be projective line

Meaning of word is supposed to be vector bundle

Under the upper suppositions, by theorem (Grothendieck) meaning is identified with direct sum of line bundles.

Language is supposed to be projective space

**P***.*^{n}Word is supposed to be projective line

**P**^{1}.Meaning of word is supposed to be vector bundle

*E*over projective line**P**^{1}.Under the upper suppositions, by theorem (Grothendieck) meaning is identified with direct sum of line bundles.

[Note 2]

L is easy sheaf of

Line bundle satisfies the following at

(i) Stalk

(ii) L is locally isomorphic with structural sheaf

*X*is algebraic manifold.*O*is module over X.^{X}L is easy sheaf of

*O*.^{X}Line bundle satisfies the following at

*L*.(i) Stalk

*L*at generating point is one-dimensional vector space over functional field_{μ}*k*(*X*).(ii) L is locally isomorphic with structural sheaf

*O*_{X}.
[Note 3]

(Replacement (i)) One-dimensional vector space over functional field

(Replacement (ii)) Locally structural sheaf

Replacement (i) and (ii) is called

(Replacement (i)) One-dimensional vector space over functional field

*k*(*X*) is replaced to*r*-dimentional.(Replacement (ii)) Locally structural sheaf

*O*is replaced to to ._{X}Replacement (i) and (ii) is called

**vector bundle of rank**or*r***locally free sheaf**.
[Note 4]

Language universal model is expressed by .

Language universal model is expressed by .

[Reference]

Vector bundle model is a description of the next paper of Aurora Theory.

Dictoron and Aurora < Language is aurora dancing above us> For SAEKI Shizuto. Tokyo, September24, 2006.

Vector bundle model is a description of the next paper of Aurora Theory.

Dictoron and Aurora < Language is aurora dancing above us> For SAEKI Shizuto. Tokyo, September24, 2006.

*Tokyo*

January 6, 2012

Sekinan Research Field of Language, 2012

January 6, 2012

Sekinan Research Field of Language, 2012

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