Saturday 6 July 2013

Vector Bundle Model

Vector Bundle Model

For SAEKI Shizuto

Pn is projective space.
P1 is projective line.
E is vector bundle over P1.
Theorem (Grothendieck)
Vector bundle E over projective line P1 is isomorphic withdirect sum of line bundles.
[Note 1]
Language is supposed to be projective space Pn.
Word is supposed to be projective line P1.
Meaning of word is supposed to be vector bundle E over projective line P1.
Under the upper suppositions, by theorem (Grothendieck) meaning is identified with direct sum of line bundles.
[Note 2]
X is algebraic manifold.
OX is module over X.
L is easy sheaf of OX.
Line bundle satisfies the following at L.
(i) Stalk Lμ at generating point is one-dimensional vector space over functional field k(X).
(ii) L is locally isomorphic with structural sheaf OX .
[Note 3]
(Replacement (i)) One-dimensional vector space over functional field k(X) is replaced to r-dimentional.
(Replacement (ii)) Locally structural sheaf OX is replaced to to .
Replacement (i) and (ii) is called vector bundle of rank r or locally free sheaf.
[Note 4]
Language universal model is expressed by .

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.

January 6, 2012
Sekinan Research Field of Language, 2012
Added at January 10, 2012
The Time of Language

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