Vector Bundle Model by Grothendieck's Theorem |
For SAEKI Shizuto and our youth days
Pn is projective space.
P1 is projective line.
E is vector bundle over P1.
P1 is projective line.
E is vector bundle over P1.
Theorem (Grothendieck)
Vector bundle E over projective line P1 is isomorphic with direct sum of line bundles.
Vector bundle E over projective line P1 is isomorphic with direct 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.
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 .
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.
(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.
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
January 6, 2012
Sekinan Research Field of Language
[Reference added, January 10, 2012]
The Time of Language
The Time of Language
